MTH102: Elementary Mathematics Ii TMA4

Question 1 : Evaluate the limitlimt→4t−√(3+4)4−t
A.−58
B.−38
C.34
D.−18

 

Question 2 : Evaluate∫e4xdx
Aex+c
B.3ex3+c
C.14e4x+c
D.13ex+c

 

Question 3 : Evaluate∫x+1×2−3x+2dx
A.3ln(x+2)−2ln(x+1)+c
B.3ln(x−2)+2ln(x+1)+c
C.3ln(x−2)−2ln(x−1)+c
D.−3ln(x−2)−2ln(x−1)+c

 

Question 4 : Determine∫x2+1(x+2)3
A.ln(x+2)+4x+2−52(x+3)2+c
B.ln(x+2)−4x+2−52(x+3)2+c
C.ln(x−2)+4x−2−52(x+3)2+c
D.−ln(x+2)−4x+2−52(x+3)2+c

 

Question 5 : Given2×5+x2−5t2, find dydx by using the first principle
A.t2+5t−3
B.6t2+10t−3
C.6t+7t−3
D. c−t−2+8t−3

 

Question 6 : Evaluate∫x2e3xdx
A.e2x3(x3−x4+29)+c
B.−e3x3(x2+2×3−29)+c
C.ex3(x2+2×3−25)+c
D.e3x3(x2−2×3+29)+c

 

Question 7 : Given f(x) =(7×4−5×3), evaluatedf(x)dx
A.7×4−5×3
B.2×3−15×2
C.28×2−15×2
D.28×3−15×2

 

Question 8 : Evaluate the limitlimx→∞2×4−x2+8x−5×4+7
A.34
B.13
C.23
D.12

 

Question 9 : Find the volume of a sphere generated by a semicircley=√(r2−x2) revolving around the x-axis
A.4πr33
B.−π−r32
C.πr34
D. 4πr32

 

Question 10 : Find the∫tan3xsec3xdx
A.sec2x
B.tan2x+1
C.cot2x+1
D.sec2x+1

 

Question 11 : Giveny(x)=x4−4×3+3×2−5x, evaluated4ydx4
A. 24
B. 42
C. 22
D. 30

 

Question 12 : Evaluate the limitlimh→02(−3+h)2−18h
A. 6
B. 8
C. 12
D. 14

 

Question 13 : Evaluate∫xe6xdx
A.x6e6x+1136e6x+c
B.x6e6x−1136e6x+c
C.x3e6x+116e6x+c
D.−x6e6x+1136e6x+c

 

Question 14 : Differentiate y=3√(x2)(2x−x2) with respect to x
A.y=5×233+4×533
B.y=10×233−8×533
C.y=10×233+8×533
D.y=5×233−4×533

 

Question 15 : Find∫sec3xtanxdx
A.cos3x2+c
B.sec3x3+c
C.cos2x+c
Dsin2x+c

 

Question 16 : Evaluate the limitlimx→−∞x2−5t−92×4+3×3
A. 1
B. 4
C. 2
D. 0

 

Question 17 : Find the derivative f(x)=2×2−16x+35 by using first principle
A.x+16
B.3x−5
C.2x−8
D.4x−16

 

Question 18 : Evaluate the limitlimx→∞6e4x−e−2x8e4x−e2x+3e−x
A.35
B.14
C.12
D.34

 

Question 19 : Find ∫xcosax2dx with respect to x
A.sin2x+c
B.sec2x+1
C.12asinax2+c
D.cos3x+c

 

Question 20 : Differentiate with respect to x:f(x)=(ax3+bx)
A.3a−b
B.3ax2+b
C.3×2+1
D.ax2+b