Math Answers

5 Find
∫sec3xtanxdx
∫sec3⁡xtan⁡xdx

sin2x+c
sin⁡2x+c

cos2x+c
cos⁡2x+c

sec3x3+c
sec3⁡x3+c

cos3x2+c
cos3⁡x2+c
6 Evaluate
∫x+1x2−3x+2dx
∫x+1x2−3x+2dx

3ln(x+2)−2ln(x+1)+c
3ln(x+2)−2ln(x+1)+c

3ln(x−2)−2ln(x−1)+c
3ln(x−2)−2ln(x−1)+c

−3ln(x−2)−2ln(x−1)+c
−3ln(x−2)−2ln(x−1)+c

3ln(x−2)+2ln(x+1)+c
3ln(x−2)+2ln(x+1)+c

3 Find
∫xcosax2dx
∫xcos⁡ax2dx
with respect to x

cos3x+c
cos3⁡x+c

sin2x+c
sin⁡2x+c

sec2x+1
sec2⁡x+1

12asinax2+c
12asin⁡ax2+c
4 Find the
∫tan3xsec3xdx
∫tan3⁡xsec3⁡xdx

tan2x+1
tan2⁡x+1

cot2x+1
cot2⁡x+1

sec2x+1
sec2⁡x+1

sec2x
sec2⁡x

1 Evaluate
∫e4xdx
∫e4xdx

14e4x+c
14e4x+c

ex+c
ex+c

3ex3+c
3ex3+c

13ex+c
13ex+c
2 Evaluate
∫xe6xdx
∫xe6xdx

x6e6x−1136e6x+c
x6e6x−1136e6x+c

x3e6x+116e6x+c
x3e6x+116e6x+c

x6e6x+1136e6x+c
x6e6x+1136e6x+c

−x6e6x+1136e6x+c
−x6e6x+1136e6x+c

1 Evaluate
∫e4xdx
∫e4xdx

14e4x+c
14e4x+c

ex+c
ex+c

3ex3+c
3ex3+c

13ex+c
13ex+c
2 Evaluate
∫xe6xdx
∫xe6xdx

x6e6x−1136e6x+c
x6e6x−1136e6x+c

x3e6x+116e6x+c
x3e6x+116e6x+c

x6e6x+1136e6x+c
x6e6x+1136e6x+c

−x6e6x+1136e6x+c
−x6e6x+1136e6x+c

A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors? Test at the .05 level of significance.

Ice Cream Flavor

A 12

B 18

C 28

D 22

9 Differentiate with respect to x:
f(x)=(ax3+bx)
f(x)=(ax3+bx)

3a−b
3a−b

ax2+b
ax2+b

3x2+1
3x2+1

3ax2+b
3ax2+b
10 Differentiate
y=3(√x2)(2x−x2)
y=3(x2)(2x−x2)
with respect to x

y=10x233−8x533
y=10x233−8x533

y=10x233+8x533
y=10x233+8x533

y=5x233−4x533
y=5x233−4x533

y=5x233+4x533
y=5x233+4x533

7 Given
2x5+x2−5t2
2x5+x2−5t2
, find
dydx
dydx
by using the first principle
c
−t−2+8t−3
−t−2+8t−3

6t+7t−3
6t+7t−3

t2+5t−3
t2+5t−3

6t2+10t−3
6t2+10t−3
8 Given
y(x)=x4−4x3+3x2−5x
y(x)=x4−4x3+3x2−5x
, evaluate
d4ydx4
d4ydx4
30
42
24
22

5 Evaluate the limit
limx→∞6e4x−e−2x8e4x−e2x+3e−x
limx→∞6e4x−e−2x8e4x−e2x+3e−x

a)34
34

b)14
14

c)12
12

d)35

6) Find the derivative
f(x)=2x2−16x+35
f(x)=2x2−16x+35
by using first principle

a) x+16
x+16

b)4x−16
4x−16

c) 3x−5
3x−5

d) 2x−8
2x−8

3 Evaluate the limit
limx→∞2x4−x2+8x−5x4+7
limx→∞2x4−x2+8x−5x4+7

a) 13

b) 23

c) 12

d) 34

4) Evaluate the limit
limx→−∞x2−5t−92x4+3x3
a) 4
b) 2
c) 0
d) 1

9) Let
h(x)=x+42x−5
find
h−1

a) h−1(x)=2+xx+5

b) h−1(x)=2+3xx−5

c) h−1(x)=4−2xx−5

d) h−1(x)=4+5x2x−5

10) Evaluate the limit
limx→0x2+4x−12x2−2x
a) 3
b) 2
c) 4
d) 0