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Calc 1 3.2

 

<== Calculus 1
Number Question Answer
See the work

1.

 

 

Algebraically find the inverse function of
ƒ(x)=4-9e^x.
f^(-1)(x)_______

 

ln((4-x)/9)

 

The work

Point Cost: 1

2.

 

 

Consider the function f(x)=3x^3.

(A) Find ƒ^(-1)(9)______

(B)Use a Theorem to find (ƒ^-1)'(9)
(ƒ^-1)'(9)=_______

(C) Calculate ƒ^(-1)(x) and
state domain and range of
f^(-1). Use interval notation.
ƒ^(-1)(x)=_______
Domain=_________
Range=________

 

(A) 1.44224957

(B) 0.0534166508

(C) =(x/3)^(1/3)             
Domain=(-∞, ∞)
Range=(-∞, ∞)

 

The work


Point Cost: 2

3.

 

Consider the function

(A) Find ______

(B)Use a Theorem to find
=_______

(C) Calculate and
state domain and range of
. Use interval notation.
=_______
Domain=_________
Range=________

 

(A) 72

(B) 16

(C) =x^(2)+8             
Domain=[0, ∞)
Range=[8, ∞)

 

The work

Point Cost: 2

4.

 

Consider the function ƒ(x)=3/(x-8)
for x > 8.

(A) Find ______

(B)Use a Theorem to find
=_______

(C) Calculate and
state domain and range of
. Use interval notation.
=_______
Domain=_________
Range=________

 

(A) 25/3

(B) 1/27

(C) =8+3/x            
Domain=(0, ∞)
Range=(8, ∞)

 

The work

Point Cost: 2

5.

 

 

 

 

 

For each of the given functions ƒ(x), find the derivative at the given point c, first find


a=_________
=_______
on the interval [7.5, ∞); c=13     
a=______
=_______

 

For c=-12
a= -1
= 1/84

For c= 13
a=9
= 1/3

The work

Point Cost: 3

6.

 

 

 

 

Evaluate the expression

 

(a) 6

(b) 2

(c) 1

The work

Point Cost: 1

7.

 

 

 

Evaluate the following expressions

 

(a) -5

(b) 4

(c) 16

(d) -4

The work

Point Cost: 1

8.

 

 

 

 

 

Use the Laws of logarithms to rewrite the expression

in a form with no logarithm of a product, quotient or power.
After rewriting we have

with the constant
A=_______
and the constant
B=________

A=4

B=4

The work

Point Cost: 2

9.

 

 

 

 

Use the Laws of logarithms to rewrite the expression
ln((xy)^(1/5))
in a form with no logarithm of a product, quotient or
power. After rewriting we have
ln((xy)^(1/5)) = Aln(x)+Bln(y)
with the constant
A=_____
and the constant
B=_____

A=1/5

B=1/5

The work

Point Cost: 2

10.

 

 

 

 

 

Use the Laws of logarithms to rewrite the expression

in a form with no logarithm of a product, quotient or power.
After rewriting we have

with
A=_______
B=_______
C=_______

A=17

B=3

C=-3

The work

Point Cost: 2

11.

 

 

 

 

 

Use the Laws of logarithms to rewrite the expression

in a form with no logarithm of a product, quotient or power.
After rewriting we have

with the constant
A=_______
the constant
B=_______
and the constant
C=_______

A=2

B=1/2

C=-1

The work

Point Cost: 2

12.

 

 

Find the solution of the exponential equation
e^(1-4x)= 8
in terms of logarithms, or correct to four decimal places.
x=_______
x= -0.269860385419959
The work

Point Cost: 1

13.

 

 

Find the solution of the logarithmic equation
19-ln(5-x)= 0
correct to four decimal places.
Your answer is
x=______
x= -178482295.963187
The work

Point Cost: 1
14.

Find the following limits.
for -∞.

(a)=0.22314355131421

(b)=-∞

The work

Point Cost: 2
15.

Evaluate the following limits

(a) ∞

(b) -∞

The work

Point Cost: 1