Download App

Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives3 Marks
Question
Evaluate:
$\lim\limits _{\text{x} \rightarrow \frac{1}{2}}\frac{4\text{x}^{2}-1}{2\text{x}-1}$
✓

Answer

Given that $\lim\limits _{\text{x} \rightarrow \frac{1}{2}}\frac{4\text{x}^{2}-1}{2\text{x}-1}$
$=\lim\limits_{\text{x} \rightarrow \frac{1}{2}}\frac{(2\text{x})^{2}-(1)^{2}}{2\text{x}-1}$
$=\lim\limits_{\text{x} \rightarrow \frac{1}{2}}\frac{(2\text{x}+1)(2\text{x}-1)}{2\text{x}-1}$ 
$=\lim\limits_{\text{x} \rightarrow \frac{1}{2}}(2\text{x}+1)$
Taking limit, We have
$=2 \times\frac{1}{2}+1$
$=1+1 $
$=2$
Hence, the answer is 2.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the letters of the word ASSASSINATION are arranged at random. Find the Probability that:
Four S’s come consecutively in the word.
→
Differentiate the following functions with respect to x:$\frac{3^\text{x}}{\text{x}+\tan\text{x}}$
→
Find the equation of the straight line passing through the point $(6, 2)$ and having slope $-3.$
→
Classify the following pairs of lines as coincident, parallel or intersecting:
x - y = 0 and 3x - 3y + 5 = 0
→
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.
→
From the employees of a company, 5 persons are selected to represents them in the managing committee of the company particulars of five persons are as follows:

S.No. Name Sex Age in years
1 Harish M 30
2 Rohan M 33
3 Sheetal F 46
4 Alice F 28
5 Salim M 41

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?

→
If $S_1, S_2, S_3$ are respectively the sum of $n, 2 n$ and $3 n$ terms of G.P. then prove that $S_1{ }^2+S_2{ }^2=S_1$ $\left(S_2+S_3\right)$.
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{100}} = 1$
→
Solve for x, the inequalities Exercises.
$\frac{|\text{x}-2|-1}{|\text{x}-2|-2}\leq0$ 
→
If ${^\text{n}}\text{C}_{12}={^\text{n}}\text{C}_{5},$ Find the value of $n.$
→