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#### Differential Calculus - Limits and Continuity Book Back Questions

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
6 x 1 = 6
1. $lim_{x\rightarrow\infty}{sin \ x \over x}$

(a)

1

(b)

0

(c)

$\infty$

(d)

-$\infty$

2. $lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx}$

(a)

2

(b)

1

(c)

-2

(d)

0

3. $lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=$

(a)

1

(b)

0

(c)

-1

(d)

$1\over 2$

4. If f(x)=x(-1)$\left\lfloor 1\over x \right\rfloor$,$x\le0$,then the value of $lim_{x\rightarrow 0}f(x)$ is equal to

(a)

-1

(b)

0

(c)

2

(d)

4

5. If f : $R \rightarrow R$ is defined by f(x)=$\left\lfloor x-3 \right\rfloor +|x-4|$ for $x \in R$, then$lim_{x\rightarrow 3^-}f(x)$ is equal to

(a)

-2

(b)

-1

(c)

0

(d)

1

6. $lim_{x \rightarrow 0}{e^{tan \ x}-e^x\over tan x-x}=$

(a)

1

(b)

e

(c)

${1\over2}$

(d)

0

7. 5 x 2 = 10
8. Complete the table using calculator and use the result to estimate the limit.
$lim_{x\rightarrow{0}}{\sqrt{x+3}-\sqrt{3}\over x}$

 x -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x)
9. Calculate $lim_{x\rightarrow3}(x^3-2x+6).$

10. Evaluate the following limits :
$lim_{x\rightarrow1}{x^m-1\over x^n-1}$ ,m and n are integers.

11. Evaluate:$lim_{x\rightarrow 0}(1+sin x)^{2 cosec x}$

12. Evaluate the following limits :$lim_{x\rightarrow \infty}(1+{1\over x})^{7x}$

13. 3 x 3 = 9
14. Calculate $\lim _{ x\rightarrow0}{|x| }$.

15. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
$lim_{x\rightarrow2}f(x)$

16. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
$lim_{x\rightarrow{1}}sin \pi x$

17. 1 x 5 = 5
18. Check if $lim_{x\rightarrow-58}f(x)$exists or not, where