Free Printable CONTINUITY AND DIFFERENTIABILITY (GAISSS)

1.

The function f (x) = |x| + |x – 1| is

a)

continuous at x = 0 as well as at x = 1.

b)

continuous at x = 1 but not at x = 0.

c)

discontinuous at x = 0 as well as at x = 1.

d)

continuous at x = 0 but not at x = 1.

2.

$Iff(x)=2x\ and\ g(x)=\frac{x^2}{2}+1,\ then\ which\ of\ the\ following\ can\ be\ a\ discontinuous\ function$

a)

$f(x)+g(x)$

b)

$f(x)-g(x)$

c)

$f(x).g(x)$

d)

$\frac{f(x)}{g(x)}$

3.

$The\ function\ f(x)=\frac{4-x^2}{4x-x^3}\ is$

a)

$discontinuous\ at\ only\ one\ point\ at\ x=0$

b)

$discontinuous\ at\ exactly\ two\ points$

c)

$discontinuous\ at\ exactly\ three\ points$

d)

$continuous\ everywhere$

4.

$Find\ the\ derivative\ of\cot^2x^3$

a)

$2\cot x^3$

b)

$-2\cot x^3\operatorname{cosec}^2x^3$

c)

$-6x^2\operatorname{cosec}^2x^3.\cot x^3$

d)

$-6x^2\operatorname{cosec}^2x^3.$

5.

$Is\ the\ function\ defined\ by\ f(x)=x^2–\sin x+5\ continuous\ at\ x=\pi?$

a)

yes

b)

no

6.

a)

a = 2, b = 1

b)

a = 1, b = 2

c)

a = 1, b = 3

d)

a = 3, b = 1

7.

Find the derivative of

a)

$\frac{1}{1+x^2}$

b)

$\frac{2}{1+x^2}$

c)

$\frac{3}{1+x^2}$

d)

$\frac{4}{1+x^2}$

8.

$Find\ \ \frac{dy}{dx}\ of\ x=a\ (\cos\theta+\theta\sin\theta),y=a(\sin\theta\ –\ \theta\cos\theta)$

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\tan\theta$

d)

$\cot\theta$

9.

$Find\ the\ \sec ond\ order\ derivative\ of\ x^{20}$

a)

$120x^{19}$

b)

$120x^{18}$

c)

$380\ x^{18}$

d)

$380\ x^{19}$

10.

$Differentiate\ \sin^2x\ w.r.t\ e^{\cos\ x}$

a)

$\frac{\cos x}{e^{\cos\ x}}$

b)

$-\frac{2\cos x}{e^{\cos x}}$

c)

$\frac{2\cos2x}{e^{\cos x}}$

d)

$-\frac{2\cos2x}{e^{\cos x}}$

11.

$Differentiate\ \sqrt{e^{\sqrt{x}}}\ ,\ x>0\ with\ respect\ to\ x.$

a)

$\frac{e^{\sqrt{x}}}{\sqrt{xe^{\sqrt{x}}}}$

b)

$\frac{e^{\sqrt{x}}}{4\sqrt{xe^{\sqrt{x}}}}$

c)

$\frac{e^{\sqrt{x}}}{-4\sqrt{xe^{\sqrt{x}}}}$

d)

$\frac{4e^{\sqrt{x}}}{\sqrt{xe^{\sqrt{x}}}}$

12.

$Differentiate\ \log_7\left(\log\ x\right)\ with\ respect\ to\ x$

a)

$\frac{1}{\log7\log x}$

b)

$\frac{\log x}{\log7\log x}$

c)

$\frac{1}{x\log7\log x}$

d)

$\frac{x}{\log7\log x}$

13.

$Differentiate\ \cot^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right]\ ,\ 0<x<\frac{\pi}{2}$

a)

$\frac{2}{3}$

b)

$\frac{1}{2}$

c)

$\frac{3}{2}$

d)

$\frac{3}{4}$

14.

$Find\ \frac{dy}{dx}\ of\ \ xy=e^{\left(x-y\right)}$

a)

$\frac{\left(y-1\right)}{x\left(y+1\right)}$

b)

$\frac{1}{x\left(y+1\right)}$

c)

$\frac{x\left(y-1\right)}{\left(y+1\right)}$

d)

$\frac{y\left(x-1\right)}{x\left(y+1\right)}$

15.

$Differentiate\ e^{x^3}$

a)

$3x^2e^{x^3}$

b)

$6x^2e^{x^3}$

c)

$3x^{ }e^{x^3}$

d)

$6x\ e^{x^3}$

CONTINUITY AND DIFFERENTIABILITY (GAISSS)

Total questions: 15

Worksheet time: 35mins

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