Free Printable 20MA1021-quiz 2

1.

The general term a_n of the sequence 1, -1, 1, -1, ... is

a)

$\left(-1\right)^{\left(n-1\right)}$

b)

$1^{\left(n-1\right)}$

c)

2n-1

d)

$\frac{1}{n}$

2.

The limit value of the sequence a_n = sinn is

a)

0

b)

$\frac{1}{\sqrt{2}}$

c)

1

d)

$\infty$

3.

The sequence

a_n=1+\frac{\left(-1\right)^n}{n}

is

a)

Oscillatory

b)

Non-convergent

c)

Convergent

d)

Divergent

4.

The series 5-4-1+5-4-1+5-4-1+.... is

a)

Convergent

b)

Oscillatory

c)

Non-convergent

d)

Non-oscillatory

5.

The series

1+\frac{1}{2}+\frac{1}{3}+...

is

a)

Convergent

b)

Non-convergent

c)

Non-divergent

d)

Divergent

6.

The value of

\lim_{n\rightarrow\infty}\frac{1}{\left(1+\frac{1}{n}\right)^n}

is

a)

$\frac{1}{e}$

b)

e

c)

$\sqrt{e}$

d)

$\frac{1}{\sqrt{e}}$

7.

If

u_n=\frac{2n-1}{n\left(n+1\right)\left(n+2\right)}

and

v_n=\frac{1}{n^2}

then

\lim_{n\rightarrow\infty}\frac{u_n}{v_n}=-----

a)

1

b)

0

c)

$\infty$

d)

2

8.

$\frac{1}{4.7.10}+\frac{4}{7.10.13}+\frac{9}{10.13.16}+...$ is

a)

$\frac{2n-1}{n\left(n+1\right)\left(n+2\right)}$

b)

$\frac{n^2}{\left(n+1\right)\left(n+4\right)\left(n+7\right)}$

c)

$\frac{n^2}{\left(3n+1\right)\left(3n+4\right)\left(3n+7\right)}$

d)

$\frac{n^2}{n\left(n+1\right)\left(n+2\right)}$

9.

$\frac{u_n}{u_{\left(n+1\right)}}=\frac{2n+1}{2n+2}$ then $\lim_{n\rightarrow\infty}n\left[\frac{u_n}{u_{\left(n+1\right)}}-1\right]$

a)

2

b)

$\frac{-1}{2}$

c)

$\frac{1}{2}$

d)

$\frac{-1}{3}$

10.

$e^{-x}=1-x+\frac{x^2}{2!}-\frac{x^3}{3!}+...$ then $\lim_{n\rightarrow\infty}\frac{u_{\left(n+1\right)}}{u_n}$

a)

0

b)

x

c)

-x

d)

1

11.

$\log\left(1+x\right)=x-\frac{x^2}{2}+\frac{x^3}{3}-...$ when x=1 is

a)

Divergent

b)

Oscillatory

c)

Convergent

d)

Non-oscillatory

12.

$\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-...$ is

a)

-1<x<1

b)

For all values of x<0

c)

For all values of x>0

d)

For all values of x

13.

$1-\frac{1}{2}+\frac{1}{3}-...$ is

a)

Divergent

b)

Conditionally convergent

c)

Absolutely converget

d)

Oscillatory

14.

$\frac{1}{\log2}-\frac{1}{\log3}+\frac{1}{\log4}-...$ find $\lim_{n\rightarrow\infty}u_n$

a)

1

b)

0

c)

-1

d)

$\infty$

15.

$\sum_{ }^{ }\left(\log n\right)^{-2n}$

a)

Limit value = 0; the series is convergent

b)

Limit value =1/e ; the series is convergent

c)

Limit value = 1/3; the series is convergent

d)

Limit value = 3; the series is divergent

16.

$\frac{u_n}{u_{\left(n+1\right)}}=\frac{e}{\left(1+\frac{1}{n}\right)^n}$ then $\lim_{n\rightarrow\infty}\left[n\log\ \frac{u_n}{u_{\left(n+1\right)}}\right]=$

a)

-1/2

b)

1/3

c)

-1/3

d)

1/2

17.

A sequence which is monotonic and bounded is called ________

a)

Divergent

b)

Convergent

c)

Infinite

d)

Oscillatory

18.

$\frac{1}{2\sqrt{1}}+\frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+...$ is

a)

$\frac{x^{2n}}{\left(n+2\right)\sqrt{n+1}}$

b)

$\frac{x^{\left(2n-2\right)}}{\left(n+1\right)\sqrt{n}}$

c)

$\frac{1}{\left(n+1\right)\sqrt{n}}$

d)

$\frac{1}{\left(n+1\right)\sqrt{n+2}}$

19.

The general term a_n of the infinite sequence 1, 1/2, 1/3,... is

a)

1/(n+2)

b)

2n-1

c)

1/n

d)

2n

20.

$u_n=\frac{n^n}{\left(n+1\right)^{\left(n+1\right)}}$ and $v_n=\frac{1}{n}$ then $\lim_{n\rightarrow\infty}\frac{u_n}{v_n}=$

a)

2

b)

1/e

c)

0

d)

e

21.

$\lim_{n\rightarrow\infty}\left(1+\frac{1}{\sqrt{n}}\right)^{\sqrt{n}}$ is

a)

e

b)

1/e

c)

$\sqrt{e}$

d)

$\frac{1}{\sqrt{e}}$

22.

The limit value of the sequence a_n=1+[2/n] is

a)

0

b)

1/2

c)

$\infty$

d)

1

23.

$\beta\left(3,4\right)=$

a)

$\int_0^1x^3\left(1-x\right)^4dx$

b)

$\int_0^1x^2\left(1-x\right)^3dx$

c)

$\int_0^1x^2\left(1+x\right)^3dx$

d)

$\int_0^{\infty}x^2\left(1-x\right)^3dx$

24.

$\Gamma\left(n+1\right)=$

a)

$\int_0^{\infty}e^{-x}x^{\left(n-1\right)}dx$

b)

$\int_0^1e^{-x}x^ndx$

c)

$\int_0^{\frac{\pi}{2}}e^{-x}x^ndx$

d)

$\int_0^{\infty}e^{-x}x^ndx$

25.

$\Gamma\left(\frac{9}{2}\right)=$

a)

$\frac{105\sqrt{\pi}}{16}$

b)

$\frac{15\sqrt{\pi}}{4}$

c)

$\frac{105\sqrt{\pi}}{8}$

d)

15/16

26.

$\beta\left(5,6\right)=$

a)

1/126

b)

144

c)

1/1260

d)

1/208

27.

$\int_0^{\frac{\pi}{2}}\sin^3x\cos^2xdx=$

a)

1/15

b)

2/15

c)

1

d)

$\frac{\sqrt{\pi}}{15}$

28.

$\int_0^{\frac{\pi}{2}}\sin^3xdx$

a)

1/3

b)

$\frac{\sqrt{\pi}}{3}$

c)

$\sqrt{\pi}$

d)

2/3

29.

$\int_0^1x^2\left(\log x\right)^4dx=$

a)

1/3

b)

-3/16

c)

$\frac{8}{3^4}$

d)

$\frac{-8}{3^4}$

30.

$\int_{ }^{ }\int_{ }^{ }\int_{ }^{ }x^{\left(l-1\right)}y^{\left(m-1\right)}z^{\left(n-1\right)}dxdydz=$

a)

$\frac{\Gamma\left(l\right)\Gamma\left(m\right)\Gamma\left(n\right)}{\Gamma\left(l+m+n+1\right)}$

b)

$\Gamma\left(l\right)\Gamma\left(m\right)\Gamma\left(n\right)$

c)

$\frac{\Gamma\left(l\right)\Gamma\left(m\right)\Gamma\left(n\right)}{\Gamma\left(l+m+n\right)}$

d)

$\frac{1}{\Gamma\left(l+m+n+1\right)}$

31.

The volume of the solid generated by the revolution about the y-axis of the area bounded by the

curve x=f(y), the y-axis is

a)

$V=\int_{ }^{ }y^2dx$

b)

$V=\int_{ }^{ }\pi y^2dx$

c)

$V=\int_{ }^{ }\pi x^2dy$

d)

$V=\int_{ }^{ }\pi ydx$

32.

The function f(x) = tanx is a periodic function with period

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$2\pi$

33.

$\left(-\pi,\pi\right)$ is

a)

$b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f\left(x\right)\cos nxdx$

b)

$b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f\left(x\right)\sin nxdx$

c)

$b_n=\frac{1}{\pi}\int_0^{2\pi}f\left(x\right)\sin nxdx$

d)

$b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f\left(x\right)dx$

34.

If a function f (x) = $x^2$ in the interval $\left(0,2\pi\right)$ then $a_0$ is

a)

$\frac{2\pi^2}{3}$

b)

0

c)

$\frac{\pi^2}{3}$

d)

$\frac{8\pi^2}{3}$

35.

$e^{-x}$ is a function in the interval $\left(-\pi,\pi\right)$ then $a_0=$

a)

$\frac{e^{\pi}-e^{-\pi}}{\pi}$

b)

$\frac{e^{-\pi}-e^{\pi}}{\pi}$

c)

$\frac{1-e^{-2\pi}}{\pi}$

d)

$\frac{1-e^{-\pi}}{\pi}$

20MA1021-quiz 2

Total questions: 35

Worksheet time: 35mins

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