Download App

Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\Big(\frac{1}{\text{x}^2+\text{x}-2}-\frac{\text{x}}{\text{x}^3-1}\Big)$
✓

Answer

$\lim\limits_{\text{x}\rightarrow1}\Big(\frac{1}{\text{x}^2+\text{x}-2}-\frac{\text{x}}{\text{x}^3-1}\Big)$$=\lim\limits_{\text{x}\rightarrow1}\Big(\frac{1}{\text{x}^2+\text{x}-2}-\frac{\text{x}}{(\text{x}-1)(\text{x}^2+\text{x}+1)}\Big)$
$=\lim\limits_{\text{x}\rightarrow1}\Big(\frac{\text{x}^3-1-\text{x}^3-\text{x}^2+2\text{x}}{(\text{x}^3-1)(\text{x}^2+\text{x}-2)}\Big)$
$=\lim\limits_{\text{x}\rightarrow1}\Bigg(\frac{\big(\text{x}^2-2\text{x}+1\big)}{\big(\text{x}^3-1\big)\big(\text{x}^2+\text{x}-2\big)}\Bigg)$
$=\lim\limits_{\text{x}\rightarrow1}\Big(\frac{(\text{x}-1)(\text{x}-1)}{(\text{x}-1)(\text{x}^2+1+\text{x})(\text{x}^2+\text{x}-2)}\Big)$
$=\lim\limits_{\text{x}\rightarrow1}\Big(\frac{\text{x}-1}{(\text{x}^2+1+\text{x})(\text{x}+2)(\text{x}-1)}\Big)$
$=\frac{1}{(1+1+1)(1+2)}$
$=\frac19$

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 "2 Marks Questions" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Given below are two statements
p : 25 is a multiple of 5.
q : 25 is a multiple of 8.
Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
→
Show the following quadratic equation:
$x^2 - (2 + i) x - (1 - 7i) = 0$
→
Solve the following system of equations in R.
$10\leq-5(\text{x}-2)<20$
→
Reduce the equation $\sqrt{3}\text{x}+\text{y}+2=0$ to:
slope-intercept form and find slope and y-intercept;
→
List all the elements of the following sets:
$\text{A} = \{\text{x : x 2} \leq 10,\text{ x} \in\text{ Z}\};$
→
Compute:
$\frac{30!}{28!}$
→
Find the perimeter of a triangle whose verticies have the coordinates $A ( 1 0 , - 2 , 8 ), B ( 8 , 0 , 7 )$ and $C (10,2,8).$
→
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
→
Evaluate $\mathop {\lim }\limits_{x \to - 1} \frac{{{x^{10}} + {x^5} + 1}}{{x - 1}}$
→
Let $R=\left\{\left(x, x^2\right): x\right.$ is a prime number less than 10$\}$
i. Write R in roster form.
ii. Find dom (R) and range (R).
→