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Test 1EEE

Total questions: 57

Worksheet time: 29mins

Name
Class
Date
1.

∫−11(x2sin⁡(3x))dx=\int_{-1}^1\left(x^2\sin\left(3x\right)\right)dx=  

(a)  

2.

The value of  ∫cos⁡5x dx\int_{ }^{ }\cos5x\ dx  =

a)

5 sin5x

b)

-5sin5x

c)

sin⁡5x5\frac{\sin5x}{5}  

d)

−sin⁡5x5-\frac{\sin5x}{5}  

3.

The value of ∫0π sin⁡3x dx\int_0^{\pi}\ \sin3x\ dx  

a)

23\frac{2}{3}  

b)

−23-\frac{2}{3}  

c)

0

d)

13\frac{1}{3}  

4.

ddx(x2) =\frac{\text{d}}{\text{d}x}\left(x^2\right)\ =  

a)

x

b)

2

c)

2x

d)

0

5.

∫02π x cos⁡nx dx =\int_0^{2\pi}\ x\ \cos nx\ dx\ =  

a)

∣x(sin⁡x)(−cos⁡x)∣\left|x\left(\sin x\right)\left(-\cos x\right)\right|  

b)

∣x(sin⁡nxn)−(−cos⁡nxn2)∣\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|  

c)

∣x(sin⁡nxn)−(−cos⁡nxn2)∣02π  =0\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|_0^{2\pi}\ \ =0  

d)

∣x(sin⁡nxn)−(−cos⁡nxn2)∣02π =2\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|_0^{2\pi}\ =2  

6.
a)

A

b)

B

c)

C

d)

D

7.
a)

A

b)

B

c)

C

d)

D

8.

The value of  ∫cos⁡5x dx\int_{ }^{ }\cos5x\ dx  =

a)

5 sin5x

b)

-5sin5x

c)

sin⁡5x5\frac{\sin5x}{5}  

d)

−sin⁡5x5-\frac{\sin5x}{5}  

9.

The value of ∫0π sin⁡3x dx\int_0^{\pi}\ \sin3x\ dx  

a)

23\frac{2}{3}  

b)

−23-\frac{2}{3}  

c)

0

d)

13\frac{1}{3}  

10.

Find the Fourier Transform of an Exponential signal

f(t)=e−atu(t),a>0f\left(t\right)=e^{-at}u\left(t\right),a>0  

a)

1a+jw\frac{1}{a+jw}  

b)

1a−jw\frac{1}{a-jw}  

c)

1−a+jw\frac{1}{-a+jw}  

d)

1−a−jw\frac{1}{-a-jw}  

11.

The Fourier Transform of a function

X(t) is X(w).X\left(t\right)\ is\ X\left(w\right).  what will be the fourier transform of  dX(t)dt\frac{\text{d}X\left(t\right)}{\text{d}t}  ?

a)

X(f)jf\frac{X\left(f\right)}{jf}  

b)

j2πfX(f)j2\pi fX\left(f\right)  

c)

dX(f)dt\frac{\text{d}X\left(f\right)}{\text{d}t}  

d)

jfX(f)jfX\left(f\right)  

12.

The Fourier Sine Transform of

e−axe-^{ax}  

a)

Fs[e−ax]=2π aa2+s2F_s\left[e-^{ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}  

b)

Fs[e−ax]=2π sa2+s2F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}  

c)

Fc[e−ax]=2π sa2+s2F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}  

d)

none of the above

13.

Fs(xf(x)) =F_s\left(xf\left(x\right)\right)\ =  

a)

dds Fc[s]\frac{d}{ds}\ F_c\left[s\right]  

b)

−dds Fc[s]-\frac{d}{ds}\ F_c\left[s\right]  

c)

dds Fs[s]\frac{d}{ds}\ F_s\left[s\right]  

d)

dds Fs[s]\frac{d}{ds}\ F_s\left[s\right]  

14.

∫eax cos⁡bx dx =\int e^{ax}\ \cos bx\ dx\ =  

a)

eaxa2+b2[acos⁡bx−bsin⁡bx]\frac{e^{ax}}{a^2+b^2}\left[a\cos bx-b\sin bx\right]  

b)

eaxa2+b2[acos⁡bx+bsin⁡bx]\frac{e^{ax}}{a^2+b^2}\left[a\cos bx+b\sin bx\right]  

c)

eaxa2+b2[bcos⁡bx+asin⁡bx]\frac{e^{ax}}{a^2+b^2}\left[b\cos bx+a\sin bx\right]  

d)

none of the above

15.

The value of

e−∞e^{-\infty}   is------------------



(a)  

16.

The Fourier Sine Transform of

e−5xe^{-5x}  

a)

Fs[e−5x]=2π 552+s2F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{5^2+s^2}  

b)

Fs[e−5x]=2π s52+s2F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{5^2+s^2}  

c)

Fs[e−5x]=2π sa2+s2F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}  

d)

none of the above

17.

The Fourier  Cosine Transform of

e−5xe^{-5x}  

a)

Fc[e−5x]=2π 552+s2F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{5^2+s^2}  

b)

Fc[e−5x]=2π s52+s2F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{5^2+s^2}  

c)

Fc[e−5x]=2π 5a2+s2F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{a^2+s^2}  

d)

none of the above

18.

Which full name is the right one for the guy of the meme ?

a)

Jean-Joseph Baptiste Fourier

b)

Jean Baptiste Joseph Fourier

c)

Charles-Henry Fourier

d)

Pierre Laplace

19.

How many Fourier's coefficients do we have ?

a)

1

b)

2

c)

3

d)

4

20.
a)
b)
c)
21.

What is the output of an inverter?

a)

DC

b)

AC

22.

a)
b)
c)
d)
23.

a)
b)
c)
d)
24.

a)
b)
c)
d)
25.

a)
b)
c)
d)
26.

a)
b)
c)
d)
27.

a)
b)
c)
d)
28.

a)
b)
c)
d)
29.

a)
b)
c)
30.

a)
b)
c)
d)
31.

a)
b)
c)
d)
32.

a)
b)
c)
d)
33.

Which one is the correct definition of Laplace Transform?

a)

F(s)=∫0∞e−stf(t)dtF\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt

b)

F(s)=∫0tf(t)g(t−u)F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)

34.

What is the Laplace Transform for f(t)=t3f\left(t\right)=t^3  ?

a)

1s3\frac{1}{s^3}  

b)

2s3\frac{2}{s^3}  

c)

6s4\frac{6}{s^4}  

d)

3s3\frac{3}{s^3}  

35.

What is Laplace Transform for e−2te^{-2t}  ?

a)

1s−2\frac{1}{s-2}  

b)

1s+2\frac{1}{s+2}  

c)

2s\frac{2}{s}  

d)

1s2\frac{1}{s^2}  

36.

What is Laplace Transform for sin⁡ 2t\sin\ 2t  ?

a)

2s2+2\frac{2}{s^2+2}  

b)

ss2+2\frac{s}{s^2+2}  

c)

2s2+4\frac{2}{s^2+4}  

d)

ss2+4\frac{s}{s^2+4}  

37.

What is Laplace Transform for 6 sin⁡ 2t6\ \sin\ 2t  ?

a)

2s2+4\frac{2}{s^2+4}  

b)

ss2+4\frac{s}{s^2+4}  

c)

6s2+4\frac{6}{s^2+4}  

d)

12s2+4\frac{12}{s^2+4}  

38.

Find L(e3tt)L\left(e^{3t}t\right)  

a)

1(s2)\frac{1}{\left(s^2\right)}  

b)

1(s−3)2\frac{1}{\left(s-3\right)^2}  

c)

1(s−2)2\frac{1}{\left(s-2\right)^2}  

d)

1(s)\frac{1}{\left(s\right)}  

39.

Find L(cos⁡ t)L\left(\cos\ t\right)  

a)

1s2+1\frac{1}{s^2+1^{ }}  

b)

1s2+4\frac{1}{s^2+4}  

c)

ss2+1\frac{s}{s^2+1}  

40.

L(∫0t e−2t (sin⁡tt)dt)L\left(\int_0^t\ ^{ }e^{-2t\ }\left(\frac{\sin t}{t}\right)dt\right)  =?

a)

1scot⁡−1(s+2)\frac{1}{s}\cot^{-1}\left(s+2\right)  

b)

1scot⁡−1(s−2)\frac{1}{s}\cot^{-1}\left(s-2\right)  

c)

scot⁡−1(s+2)s\cot^{-1}\left(s+2\right)  

d)

scot⁡−1s−2s\cot^{-1}s-2  

41.

L−1(1s2−5s+6)L^{-1}\left(\frac{1}{s^2-5s+6}\right)  = ?

a)

e3t−e2te^{3t}-e^{2t}  

b)

2e52t(sinh⁡ 12t)2e^{\frac{5}{2}t}\left(\sinh\ \frac{1}{2}t\right)  

c)

e2t−e3te^{2t}-e^{3t}  

d)

e3t+e2te^{3t}+e^{2t}  

42.

a)
b)
c)
d)
43.

What is Laplace Transform for e−2te^{-2t}  ?

a)

1s−2\frac{1}{s-2}  

b)

1s+2\frac{1}{s+2}  

c)

2s\frac{2}{s}  

d)

1s2\frac{1}{s^2}  

44.

Encontrar la Transformada de Laplace de la siguiente función

a)
b)
c)
d)
45.

Find: L{e2t}L\left\{e^{2t}\right\}

a)

2s+2\frac{\text{2}}{\text{s+2}}  

b)

1s−2\frac{1}{s-2}  

c)

1s+2\frac{1}{s+2}

d)

1s−1\frac{1}{s-1}  

46.

L{5}L\left\{5\right\}  

Find:

a)

15s\frac{1}{5s}  

b)

5s5s  

c)

5s\frac{5}{s}  

d)

s5\frac{s}{5}  

47.

Find: L{sin⁡3t}L\left\{\sin3t\right\}  


a)

1s+3\frac{1}{s+3}  

b)

1s2−9\frac{1}{s^2-9}  

c)

3s2+9\frac{3}{s^2+9}  

d)

3s2−9\frac{3}{s^2-9}  

48.

Find: L{2t}L\left\{2t\right\}  


a)

2s2\frac{2}{s^2}  

b)

1s2\frac{1}{s^2}  

c)

12s2\frac{1}{2s^2}  

d)

s22\frac{s^2}{2}  

49.

Find L−1(ss2+25)L^{-1}\left(\frac{s}{s^2+25}\right)  

a)

cos 25t

b)

sin 5t

c)

cos 5t

50.

Find L−1(1s2+1)L^{-1}\left(\frac{1}{s^2+1}\right)  

a)

sin t

b)

sin 5t

c)

cos t

51.

L−1(1(s−3)2)L^{-1}\left(\frac{1}{\left(s-3\right)^2}\right)  

a)

e2tte^{2t}t  

b)

ett2e^tt^2  

c)

e3tte^{3t}t  

52.

s2+2s+5s^2+2s+5  Complete the square

a)

(s+4)2+2\left(s+4\right)^2+2  

b)

(s+2)2+4\left(s+2\right)^2+4  

c)

(s+2)2+16\left(s+2\right)^2+16  

53.

จงหาค่าผลการแปลงลาปลาซ L{f(t)}=F(s) กำหนดให้  f(t)=−2f\left(t\right)=-2  

a)

2S\frac{2}{S}

b)

−2S\frac{-2}{S}

c)

12S\frac{1}{2S}

d)

S2\frac{S}{2}

e)

S−2\frac{S}{-2}

54.

จงหาค่าผลการแปลงลาปลาซ L{f(t)}=F(s) กำหนดให้ f(t)=  2t22t^2   

a)

2S2\frac{2}{S^2}  

b)

4S3\frac{4}{S^3}  

c)

2S3\frac{2}{S^3}  

d)

4S2\frac{4}{S^2}  

e)

1S2\frac{1}{S^2}  

55.

จงหาค่าผลการแปลงลาปลาซ L{f(t)}=F(s) กำหนดให้ f(t)=3cos(2t)

a)

6S2+4\frac{6}{S^2+4}

b)

3SS2+4\frac{3S}{S^2+4}

c)

6S2+2\frac{6}{S^2+2}

d)

3SS2+2\frac{3S}{S^2+2}

e)

SS2+2\frac{S}{S^2+2}

56.

จงหาค่าผลการแปลงลาปลาซผกผันกำหนดให้ F(s)=  13S\frac{1}{3S}  

a)

13\frac{1}{3}  

b)

33  

c)

13t\frac{1}{3t}  

d)

13S\frac{1}{3S}  

e)

3t3t  

57.

จงหาค่าผลการแปลงลาปลาซ L{f(t)}=F(s) กำหนดให้ f(t)=  e3tsin⁡(2t)e^{3t}\sin\left(2t\right)  

a)

2(S−3)2+4\frac{2}{\left(S-3\right)^2+4}  

b)

2(S+3)2+4\frac{2}{\left(S+3\right)^2+4}  

c)

4(S−3)2+2\frac{4}{\left(S-3\right)^2+2}  

d)

4(S+3)2+2\frac{4}{\left(S+3\right)^2+2}  

e)

3(S−3)2+4\frac{3}{\left(S-3\right)^2+4}  

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