How do i calculate $lim_{hto0}frac{f(a+h^2)-f(a+h)}{h}$?












5












$begingroup$


All do i know about this problem is that f can be derived in "a".



What troubles me is the h squared,i just can't get rid of it or make it useful,no matter what i do, i always end up with it giving me an undefined limit, so it stays like that,any idea on how to get rid of it? or any rule i can use to make this easy?






calculus limits derivatives







share|cite|improve this question











$endgroup$

















    5












    $begingroup$


    All do i know about this problem is that f can be derived in "a".



    What troubles me is the h squared,i just can't get rid of it or make it useful,no matter what i do, i always end up with it giving me an undefined limit, so it stays like that,any idea on how to get rid of it? or any rule i can use to make this easy?






    calculus limits derivatives







    share|cite|improve this question











    $endgroup$















      5












      5








      5


      1



      $begingroup$


      All do i know about this problem is that f can be derived in "a".



      What troubles me is the h squared,i just can't get rid of it or make it useful,no matter what i do, i always end up with it giving me an undefined limit, so it stays like that,any idea on how to get rid of it? or any rule i can use to make this easy?






      calculus limits derivatives







      share|cite|improve this question











      $endgroup$




      All do i know about this problem is that f can be derived in "a".



      What troubles me is the h squared,i just can't get rid of it or make it useful,no matter what i do, i always end up with it giving me an undefined limit, so it stays like that,any idea on how to get rid of it? or any rule i can use to make this easy?






      calculus limits derivatives




      calculus limits derivatives






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 31 at 21:51







      Salah Gaming

















      asked Jan 31 at 21:48









      Salah GamingSalah Gaming

      293




      293






















          3 Answers
          3






          active

          oldest

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          10












          $begingroup$

          You can write
          $$frac{f(a + h^2) - f(a+h)}{h} = h cdot frac{f(a+h^2) - f(a)}{h^2} - frac{f(a+h) - f(a)}{h}$$
          and compute these two limits individually.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            yup worked,thanks a lot!
            $endgroup$
            – Salah Gaming
            Jan 31 at 21:58



















          6












          $begingroup$

          This is
          $$lim_{hto0}frac{f(a+h^2)-f(a)}{h}-lim_{hto0}frac{f(a+h)-f(a)}{h}.$$
          If $f'(a)$ exists, this is
          $$lim_{hto0}hleft(frac{f(a+h^2)-f(a)}{h^2}right)-f'(a)=-f'(a).$$






          share|cite|improve this answer









          $endgroup$





















            3












            $begingroup$

            Hint:$$lim_{hto0}frac{f(a+h^2)-f(a)}h=lim_{hto0}hfrac{f(a+h^2)-f(a)}{h^2}=htimes f'(a)=0.$$






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
              $endgroup$
              – fleablood
              Jan 31 at 21:57










            • $begingroup$
              Thanks btw u helped me a lot!
              $endgroup$
              – Salah Gaming
              Jan 31 at 21:58










            • $begingroup$
              I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
              $endgroup$
              – John Omielan
              Jan 31 at 22:06










            • $begingroup$
              @fleablood Yes, it is fine, as long as both limits exist.
              $endgroup$
              – José Carlos Santos
              Jan 31 at 22:10






            • 1




              $begingroup$
              No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
              $endgroup$
              – José Carlos Santos
              Jan 31 at 22:30












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            3 Answers
            3






            active

            oldest

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            3 Answers
            3






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            10












            $begingroup$

            You can write
            $$frac{f(a + h^2) - f(a+h)}{h} = h cdot frac{f(a+h^2) - f(a)}{h^2} - frac{f(a+h) - f(a)}{h}$$
            and compute these two limits individually.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              yup worked,thanks a lot!
              $endgroup$
              – Salah Gaming
              Jan 31 at 21:58
















            10












            $begingroup$

            You can write
            $$frac{f(a + h^2) - f(a+h)}{h} = h cdot frac{f(a+h^2) - f(a)}{h^2} - frac{f(a+h) - f(a)}{h}$$
            and compute these two limits individually.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              yup worked,thanks a lot!
              $endgroup$
              – Salah Gaming
              Jan 31 at 21:58














            10












            10








            10





            $begingroup$

            You can write
            $$frac{f(a + h^2) - f(a+h)}{h} = h cdot frac{f(a+h^2) - f(a)}{h^2} - frac{f(a+h) - f(a)}{h}$$
            and compute these two limits individually.






            share|cite|improve this answer









            $endgroup$



            You can write
            $$frac{f(a + h^2) - f(a+h)}{h} = h cdot frac{f(a+h^2) - f(a)}{h^2} - frac{f(a+h) - f(a)}{h}$$
            and compute these two limits individually.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jan 31 at 21:52









            Umberto P.Umberto P.

            40.3k13370




            40.3k13370












            • $begingroup$
              yup worked,thanks a lot!
              $endgroup$
              – Salah Gaming
              Jan 31 at 21:58


















            • $begingroup$
              yup worked,thanks a lot!
              $endgroup$
              – Salah Gaming
              Jan 31 at 21:58
















            $begingroup$
            yup worked,thanks a lot!
            $endgroup$
            – Salah Gaming
            Jan 31 at 21:58




            $begingroup$
            yup worked,thanks a lot!
            $endgroup$
            – Salah Gaming
            Jan 31 at 21:58











            6












            $begingroup$

            This is
            $$lim_{hto0}frac{f(a+h^2)-f(a)}{h}-lim_{hto0}frac{f(a+h)-f(a)}{h}.$$
            If $f'(a)$ exists, this is
            $$lim_{hto0}hleft(frac{f(a+h^2)-f(a)}{h^2}right)-f'(a)=-f'(a).$$






            share|cite|improve this answer









            $endgroup$


















              6












              $begingroup$

              This is
              $$lim_{hto0}frac{f(a+h^2)-f(a)}{h}-lim_{hto0}frac{f(a+h)-f(a)}{h}.$$
              If $f'(a)$ exists, this is
              $$lim_{hto0}hleft(frac{f(a+h^2)-f(a)}{h^2}right)-f'(a)=-f'(a).$$






              share|cite|improve this answer









              $endgroup$
















                6












                6








                6





                $begingroup$

                This is
                $$lim_{hto0}frac{f(a+h^2)-f(a)}{h}-lim_{hto0}frac{f(a+h)-f(a)}{h}.$$
                If $f'(a)$ exists, this is
                $$lim_{hto0}hleft(frac{f(a+h^2)-f(a)}{h^2}right)-f'(a)=-f'(a).$$






                share|cite|improve this answer









                $endgroup$



                This is
                $$lim_{hto0}frac{f(a+h^2)-f(a)}{h}-lim_{hto0}frac{f(a+h)-f(a)}{h}.$$
                If $f'(a)$ exists, this is
                $$lim_{hto0}hleft(frac{f(a+h^2)-f(a)}{h^2}right)-f'(a)=-f'(a).$$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 31 at 21:52









                Lord Shark the UnknownLord Shark the Unknown

                108k1162136




                108k1162136























                    3












                    $begingroup$

                    Hint:$$lim_{hto0}frac{f(a+h^2)-f(a)}h=lim_{hto0}hfrac{f(a+h^2)-f(a)}{h^2}=htimes f'(a)=0.$$






                    share|cite|improve this answer









                    $endgroup$













                    • $begingroup$
                      Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                      $endgroup$
                      – fleablood
                      Jan 31 at 21:57










                    • $begingroup$
                      Thanks btw u helped me a lot!
                      $endgroup$
                      – Salah Gaming
                      Jan 31 at 21:58










                    • $begingroup$
                      I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                      $endgroup$
                      – John Omielan
                      Jan 31 at 22:06










                    • $begingroup$
                      @fleablood Yes, it is fine, as long as both limits exist.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:10






                    • 1




                      $begingroup$
                      No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:30
















                    3












                    $begingroup$

                    Hint:$$lim_{hto0}frac{f(a+h^2)-f(a)}h=lim_{hto0}hfrac{f(a+h^2)-f(a)}{h^2}=htimes f'(a)=0.$$






                    share|cite|improve this answer









                    $endgroup$













                    • $begingroup$
                      Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                      $endgroup$
                      – fleablood
                      Jan 31 at 21:57










                    • $begingroup$
                      Thanks btw u helped me a lot!
                      $endgroup$
                      – Salah Gaming
                      Jan 31 at 21:58










                    • $begingroup$
                      I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                      $endgroup$
                      – John Omielan
                      Jan 31 at 22:06










                    • $begingroup$
                      @fleablood Yes, it is fine, as long as both limits exist.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:10






                    • 1




                      $begingroup$
                      No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:30














                    3












                    3








                    3





                    $begingroup$

                    Hint:$$lim_{hto0}frac{f(a+h^2)-f(a)}h=lim_{hto0}hfrac{f(a+h^2)-f(a)}{h^2}=htimes f'(a)=0.$$






                    share|cite|improve this answer









                    $endgroup$



                    Hint:$$lim_{hto0}frac{f(a+h^2)-f(a)}h=lim_{hto0}hfrac{f(a+h^2)-f(a)}{h^2}=htimes f'(a)=0.$$







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Jan 31 at 21:52









                    José Carlos SantosJosé Carlos Santos

                    173k23133241




                    173k23133241












                    • $begingroup$
                      Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                      $endgroup$
                      – fleablood
                      Jan 31 at 21:57










                    • $begingroup$
                      Thanks btw u helped me a lot!
                      $endgroup$
                      – Salah Gaming
                      Jan 31 at 21:58










                    • $begingroup$
                      I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                      $endgroup$
                      – John Omielan
                      Jan 31 at 22:06










                    • $begingroup$
                      @fleablood Yes, it is fine, as long as both limits exist.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:10






                    • 1




                      $begingroup$
                      No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:30


















                    • $begingroup$
                      Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                      $endgroup$
                      – fleablood
                      Jan 31 at 21:57










                    • $begingroup$
                      Thanks btw u helped me a lot!
                      $endgroup$
                      – Salah Gaming
                      Jan 31 at 21:58










                    • $begingroup$
                      I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                      $endgroup$
                      – John Omielan
                      Jan 31 at 22:06










                    • $begingroup$
                      @fleablood Yes, it is fine, as long as both limits exist.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:10






                    • 1




                      $begingroup$
                      No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                      $endgroup$
                      – José Carlos Santos
                      Jan 31 at 22:30
















                    $begingroup$
                    Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                    $endgroup$
                    – fleablood
                    Jan 31 at 21:57




                    $begingroup$
                    Can you explain why it would be kosher to say $lim h[K(h^2)] = lim h(lim K(w)) = lim h*f'(x) = 0$? Is it okay to split a limit that way.
                    $endgroup$
                    – fleablood
                    Jan 31 at 21:57












                    $begingroup$
                    Thanks btw u helped me a lot!
                    $endgroup$
                    – Salah Gaming
                    Jan 31 at 21:58




                    $begingroup$
                    Thanks btw u helped me a lot!
                    $endgroup$
                    – Salah Gaming
                    Jan 31 at 21:58












                    $begingroup$
                    I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                    $endgroup$
                    – John Omielan
                    Jan 31 at 22:06




                    $begingroup$
                    I see you using "$fleft(a + h^2right) - fleft(aright)$" in the numerator compared to the question's "$fleft(a + h^2right) - fleft(a + hright)$" based on the value split, but you may wish to make this clear in your answer.
                    $endgroup$
                    – John Omielan
                    Jan 31 at 22:06












                    $begingroup$
                    @fleablood Yes, it is fine, as long as both limits exist.
                    $endgroup$
                    – José Carlos Santos
                    Jan 31 at 22:10




                    $begingroup$
                    @fleablood Yes, it is fine, as long as both limits exist.
                    $endgroup$
                    – José Carlos Santos
                    Jan 31 at 22:10




                    1




                    1




                    $begingroup$
                    No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                    $endgroup$
                    – José Carlos Santos
                    Jan 31 at 22:30




                    $begingroup$
                    No, my answer is not $0$. I did not provide an answer. I provided a hint to help the OP to obtain the answer.
                    $endgroup$
                    – José Carlos Santos
                    Jan 31 at 22:30


















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