Calculus Answers

Determine if the following function is even, odd, or neither.

f(x) = -9x4 + 5x + 3

Integrate with respect to x :
∫41x+1x√dx

1. Integrate with respect to x :
∫2−1x2(x3+4)2dx

2. Integrate with respect to x :
∫2−1x2(x3+4)2dx

3. Integrate with respect to x :
∫3−1x7+x2−−−−−√dx

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

3) Given that
f(x)=2x2−3x+5
, evaluate
f(x+Δx)Δx

a) 2x−1+Δx

b) −2x−3+Δx

c) 2x−2+Δx

d) 4x−3+2Δx

4) Let
f(x)=x2+2
and
g(x)=x2+3
. Find the composite function
f(g(x))

a) x2+4x2+6

b) x4+6x2+11

c) x4−3x2+6

d) x2−3x2+8

Describe the long term behaviour of the sequence x(to the base n) given by x(to base n)=11x(0.9)^n -5 (n=1,2,3...)
Justify answer