Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Using the method of L' Hospital, evaluate the limit.  <img alt="\lim _{x \rightarrow 1} \frac{\left(3 x^{2}+2 x-5\right)}{\left(x^{2}-1\right)}" src="https://entrancecorner.oncodecogs

Using the method of L' Hospital, evaluate the limit.  \lim _{x \rightarrow 1} \frac{\left(3 x^{2}+2 x-5\right)}{\left(x^{2}-1\right)}

Option: 1

-4


Option: 2

2


Option: 3

4


Option: 4

0


Answers (1)

best_answer

Apply the L' Hospital's Rule, when \lim _{x \rightarrow 0} \frac{f(x)}{g(x)}=\frac{0}{0}, \frac{\infty}{\infty}, etc. [an intermediate form] in the following way

- Differentiate \lim _{x \rightarrow a} \frac{f(x)}{g(x)}=\lim _{x \rightarrow a} \frac{f^{\prime}(x)}{g^{\prime}(x)}, provided that the limit \lim _{x \rightarrow a} \frac{f^{\prime}(x)}{g^{\prime}(x)} exists.

- Otherwise, go on differentiating till the limit with the determinate form is achieved.

The provided limit is

\lim _{x \rightarrow 1} \frac{\left(3 x^{2}+2 x-5\right)}{\left(x^{2}-1\right)}=\frac{0}{0}

Here use the L' Hospital rule and also refer to the following formula.

\frac{d}{d x} x^{n}=n x^{n-1}

Now, derive the following: 

$$ \begin{aligned} & \lim _{x \rightarrow 1} \frac{\left(3 x^{2}+2 x-5\right)}{\left(x^{2}-1\right)} \\ & =\lim _{x \rightarrow 1} \frac{\frac{d}{d x}\left(3 x^{2}+2 x-5\right)}{\frac{d}{d x}\left(x^{2}-1\right)} \\ & =\lim _{x \rightarrow 1} \frac{(3 \times 2 x+2)}{(2 x)} \\ & =\lim _{x \rightarrow 1} \frac{(6 x+2)}{(2 x)} \\ \end{aligned}

$$ \begin{aligned} & =\frac{(6 \times 1+2)}{(2 \times 1)} \\ & =4 \end{aligned}

Posted by

Info Expert 30

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Is it difficult to get into NIT Durgapur? JEE Main cut-offs for BTech programmes
anam-khan

JEE Main Deleted Syllabus 2025: Topics to skip this year; why no optional questions?
anam-khan

NTA Exam 2025 Live: UGC NET admit card out for all exams; JEE Main session 1 hall ticket soon

Latest Question