Deck 3: Extension B: Differentiation Rules

Question 1

Solve each equation for x.
(a) (b)

Answer 1

,

Question 2

Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 5 - ln (x + 6)

A)
B)
C)
D)

Answer 2

Question 3

Determine whether f is one-to-one.

Answer 3

Yes

Question 4

Use the laws of logarithms to expand the expression. ln

A) ln
B) ln (x + 5) - ln (x - 6)
C) ln [(x + 5)(x - 6)]
D) ln

Question 5

The graph of f is given.Sketch the graph of f^-1 on the same set of axes.

Question 6

When a camera flash goes off,the batteries immediately begin to recharge the flash's capacitor,which stores electric charge given by (The maximum charge capacity is and t is measured in seconds.)How long does it take to recharge the capacitor to 90% of capacity if ?

A) seconds
B) seconds
C) seconds
D) seconds
E) seconds

Question 7

Solve the equation.

A) x = ln + 2
B) x = ln - 2
C) x = ln + 2
D) x = ln - 2

Question 8

Find the exact value of the expression.

A) 2
B) 4
C) 1
D) 5
E) 3

Question 9

Find the domain,range,and x-intercept(s)of the function.

Question 10

Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch.How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

A) 13,014,952 mi
B) 13015052.4 mi
C) 5.2 mi
D) 13,015,152 mi
E) 1084587.7 mi

Question 11

Find a formula for the inverse of the function.

A)
B)
C)
D)
E)