Mixing
$limlimits_{x to 0} frac{sqrt{(a^4+(bx)^2} - sqrt{a^4+b}}{x}$
$begingroup$
calculate...
this is my homework
the photo is my solution proposal but I don't know what to do next....
limits analysis functions
edited Jan 15 at 23:27
user376343
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
$endgroup$
add a comment |
$begingroup$
calculate...
this is my homework
the photo is my solution proposal but I don't know what to do next....
limits analysis functions
edited Jan 15 at 23:27
user376343
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
$endgroup$
2
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00
add a comment |
$begingroup$
calculate...
this is my homework
the photo is my solution proposal but I don't know what to do next....
limits analysis functions
edited Jan 15 at 23:27
user376343
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
$endgroup$
calculate...
this is my homework
the photo is my solution proposal but I don't know what to do next....
limits analysis functions
limits analysis functions
edited Jan 15 at 23:27
user376343
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
edited Jan 15 at 23:27
user376343
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
edited Jan 15 at 23:27
user376343
3,7883828
edited Jan 15 at 23:27
user376343
3,7883828
edited Jan 15 at 23:27
user376343
3,7883828
3,7883828
asked Jan 15 at 19:25
mona1lisamona1lisa
337
asked Jan 15 at 19:25
mona1lisamona1lisa
337
asked Jan 15 at 19:25
mona1lisamona1lisa
337
337
2
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00
add a comment |
2
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00
2
2
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$$sqrt{a^4+b^2x^2}-sqrt{a^4+b}rightarrow a^2-sqrt{a^4+b}.$$
If $bneq0$ then the limit does not exist.
If $b=0$ then the limit is equal to $0$.
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$frac{x^2left(b^2-frac{b}{x^2}right)}{pm xleft(sqrt{frac{a^4}{x^2}+b^2}+sqrt{frac{a^2}{x^2}+frac{b}{x^2}}right)}$$
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$sqrt{a^4+b^2x^2}-sqrt{a^4+b}rightarrow a^2-sqrt{a^4+b}.$$
If $bneq0$ then the limit does not exist.
If $b=0$ then the limit is equal to $0$.
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
$endgroup$
add a comment |
$begingroup$
$$sqrt{a^4+b^2x^2}-sqrt{a^4+b}rightarrow a^2-sqrt{a^4+b}.$$
If $bneq0$ then the limit does not exist.
If $b=0$ then the limit is equal to $0$.
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
$endgroup$
add a comment |
$begingroup$
$$sqrt{a^4+b^2x^2}-sqrt{a^4+b}rightarrow a^2-sqrt{a^4+b}.$$
If $bneq0$ then the limit does not exist.
If $b=0$ then the limit is equal to $0$.
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
$endgroup$
$$sqrt{a^4+b^2x^2}-sqrt{a^4+b}rightarrow a^2-sqrt{a^4+b}.$$
If $bneq0$ then the limit does not exist.
If $b=0$ then the limit is equal to $0$.
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
answered Jan 15 at 19:36
Michael RozenbergMichael Rozenberg
104k1892197
104k1892197
add a comment |
add a comment |
$begingroup$
Write your term in the form
$$frac{x^2left(b^2-frac{b}{x^2}right)}{pm xleft(sqrt{frac{a^4}{x^2}+b^2}+sqrt{frac{a^2}{x^2}+frac{b}{x^2}}right)}$$
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$frac{x^2left(b^2-frac{b}{x^2}right)}{pm xleft(sqrt{frac{a^4}{x^2}+b^2}+sqrt{frac{a^2}{x^2}+frac{b}{x^2}}right)}$$
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$frac{x^2left(b^2-frac{b}{x^2}right)}{pm xleft(sqrt{frac{a^4}{x^2}+b^2}+sqrt{frac{a^2}{x^2}+frac{b}{x^2}}right)}$$
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
$endgroup$
Write your term in the form
$$frac{x^2left(b^2-frac{b}{x^2}right)}{pm xleft(sqrt{frac{a^4}{x^2}+b^2}+sqrt{frac{a^2}{x^2}+frac{b}{x^2}}right)}$$
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
answered Jan 15 at 19:40
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
75.9k42866
75.9k42866
add a comment |
add a comment |
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2
$begingroup$
Are you sure you copied the problem correctly? As you wrote it in the question it's not "indeterminate"; the nummerator has a non-zero limit. Seems like $lim(sqrt{a^4+(bx)^2}-sqrt{a^4})/x$ would be a better question
$endgroup$
– David C. Ullrich
Jan 15 at 19:31
$begingroup$
Please, no picture. Typeset your solution.
$endgroup$
– Yves Daoust
Jan 15 at 20:00