Mixing
Find the limit of rational function
$begingroup$
I have this rational function
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}
$
And i really don't know where to start to solve it.
So if you can give me some tips on solving this i would really appreciate it.
real-analysis limits
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
$endgroup$
add a comment |
$begingroup$
I have this rational function
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}
$
And i really don't know where to start to solve it.
So if you can give me some tips on solving this i would really appreciate it.
real-analysis limits
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
$endgroup$
add a comment |
$begingroup$
I have this rational function
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}
$
And i really don't know where to start to solve it.
So if you can give me some tips on solving this i would really appreciate it.
real-analysis limits
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
$endgroup$
I have this rational function
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}
$
And i really don't know where to start to solve it.
So if you can give me some tips on solving this i would really appreciate it.
real-analysis limits
real-analysis limits
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
edited Jan 29 at 9:23
YuiTo Cheng
2,1862937
2,1862937
asked Jan 29 at 9:19
krnekikrneki
82
asked Jan 29 at 9:19
krnekikrneki
82
asked Jan 29 at 9:19
krnekikrneki
82
82
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint:let $sqrt{x+2}=a,sqrt{x+7}=b$ and $sqrt{4x+1}=c$
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}=lim_{x to2}frac{(a-2)(b-3)}{(x-2)(c-3)}
$
Do you know what to do now?
answered Jan 29 at 9:24
abc...abc...
3,237739
$endgroup$
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:let $sqrt{x+2}=a,sqrt{x+7}=b$ and $sqrt{4x+1}=c$
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}=lim_{x to2}frac{(a-2)(b-3)}{(x-2)(c-3)}
$
Do you know what to do now?
answered Jan 29 at 9:24
abc...abc...
3,237739
$endgroup$
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
add a comment |
$begingroup$
Hint:let $sqrt{x+2}=a,sqrt{x+7}=b$ and $sqrt{4x+1}=c$
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}=lim_{x to2}frac{(a-2)(b-3)}{(x-2)(c-3)}
$
Do you know what to do now?
answered Jan 29 at 9:24
abc...abc...
3,237739
$endgroup$
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
add a comment |
$begingroup$
Hint:let $sqrt{x+2}=a,sqrt{x+7}=b$ and $sqrt{4x+1}=c$
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}=lim_{x to2}frac{(a-2)(b-3)}{(x-2)(c-3)}
$
Do you know what to do now?
answered Jan 29 at 9:24
abc...abc...
3,237739
$endgroup$
Hint:let $sqrt{x+2}=a,sqrt{x+7}=b$ and $sqrt{4x+1}=c$
$
lim_{x to2} frac{sqrt{x+2}sqrt{x+7}-2sqrt{x+7}-3sqrt{x+2}+6}{xsqrt{4x+1}-2sqrt{4x+1}-3x+6}=lim_{x to2}frac{(a-2)(b-3)}{(x-2)(c-3)}
$
Do you know what to do now?
answered Jan 29 at 9:24
abc...abc...
3,237739
answered Jan 29 at 9:24
abc...abc...
3,237739
answered Jan 29 at 9:24
abc...abc...
3,237739
answered Jan 29 at 9:24
abc...abc...
3,237739
3,237739
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
add a comment |
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
I know now what to do, but can you please explain where did number 6 go?
$endgroup$
– krneki
Jan 29 at 9:36
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
$begingroup$
Note that (a-2)(b-3)=ab-2b-3a+6
$endgroup$
– abc...
Jan 29 at 20:58
add a comment |
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