Vidaara.orgClass 11 · Mathematics
CodeVID-M11-12-LIM-01
Idea & Algebra of Limits — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$\displaystyle\lim_{x\to2}(x+1)=$
- A.$2$
- B.$3$
- C.$1$
- D.$0$
2.
$\displaystyle\lim_{x\to a} c=$
- A.$0$
- B.$c$
- C.$a$
- D.$\infty$
3.
$\displaystyle\lim_{x\to3} x^2=$
- A.$6$
- B.$9$
- C.$3$
- D.$0$
4.
$\displaystyle\lim_{x\to0}(5)=$
- A.$0$
- B.$5$
- C.$\infty$
- D.undefined
5.
$\displaystyle\lim\big(f(x)\,g(x)\big)=$
- A.$\lim f+\lim g$
- B.$(\lim f)(\lim g)$
- C.$\lim f-\lim g$
- D.$0$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $\displaystyle\lim_{x\to1}(2x+3)$.
7.
Evaluate $\displaystyle\lim_{x\to2}(x^2-1)$.
8.
Evaluate $\displaystyle\lim_{x\to0}(3x+2)$.
9.
Evaluate $\displaystyle\lim_{x\to3}\dfrac{x^2-9}{x-3}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Evaluate $\displaystyle\lim_{x\to2}\dfrac{x^2-4}{x-2}$.
11.
Evaluate $\displaystyle\lim_{x\to1}\dfrac{x^3-1}{x-1}$.
12.
Evaluate $\displaystyle\lim_{x\to0}\dfrac{\sqrt{x+1}-1}{x}$.
13.
Evaluate $\displaystyle\lim_{x\to2}\dfrac{x^2+3x-10}{x-2}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Evaluate $\displaystyle\lim_{x\to3}\dfrac{x^2-9}{x^2-x-6}$.
15.
Evaluate $\displaystyle\lim_{x\to0}\dfrac{\sqrt{1+x}-\sqrt{1-x}}{x}$.
Answer Key
Section A — Multiple Choice Questions
- (B) $3$
- (B) $c$
- (B) $9$
- (B) $5$
- (B) $(\lim f)(\lim g)$
Section B — Short Answer (2 marks)
- $5$.
- $3$.
- $2$.
- $6$.
Section C — Short Answer (3 marks)
- $4$.
- $3$.
- $\tfrac12$.
- $7$.
Section D — Long Answer (5 marks)
- $\tfrac65$.
- $1$.
Generated by Vidaara.org · Assignment VID-M11-12-LIM-01 · vidaara.org