Question

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Question 2 For the following limit, choose the correct answer. x? + 4x - 7 lim X- e4x + 6 After applying L'Hospital's Rule once, what will you get? 2x + 4 lim *-* 4 e Tim 2x lim No need to apply L'Hospital's Rule

Answer 1

Given data:

+ 4.C 7 lim 100 => 4r+6

We need to apply L' Hospital rule once,

We know that by L' Hospitals rule we can calculate the limit that may otherwise so hard.

L' Hospitals rule:

$\lim_{x\rightarrow c}(\frac{f(x)}{g(x)})=\lim_{x\rightarrow c}(\frac{f'(x)}{g'(x)})$

Where f'(x) and g'(x) are the derivatives of the numerator and denominator.

Here $f(x)=x^{2}+4x-7$    and

. e

$f'(x)=\frac{d}{dx}f(x)=\frac{d}{dx}(x^{2}+4x-7)=2x+4$

$g'(x)=\frac{d}{dx}g(x)=\frac{d}{dx}(e^{4x+6})=e^{4x+6}.\frac{d}{dx}(4x+6)=4e^{4x+6}$

Therefore , the result after applying L'Hospital rule is

$\lim_{x\rightarrow \infty}(\frac{2x+4}{4e^{4x+6}})$

So the answer is first option.Finally this is the answer and if you have any doubts please let me know in the comment section.Thank you.