Test 1 Review

Difference Quotient

100

Find the difference quotient for the function: f(x)=3x+2

3

200

Find the difference quotient for the function:

f(x)=x²-4x

2x+h-4

300

Find the difference quotient for the function:

f(x)=-2x²+4x-6

-4x-2h+4

Trig

100

Evaluate cos(11π/6).

√3/2

200

Evaluate cot(π/4).

1

300

Evaluate arccos(-√2/2).

3π/4

Rate of Change

100

A car's position at t = 2s is s=10m, and at t=5s its 25m. Find the average rate of change of position from t=2 to t=5.

5m/s

200

s(t) represents the position of an object at time t moving along a line. Suppose s(3) = 128 and s(8) = 62. Find the average velocity of the object over the interval time [3,8].

-13.2

300

Consider the function: f(x)=x²-4x+1. Find the average rate of change on the interval [3,7].

6

Limits

100

Find the following limit: lim x->0 (sinx²)+(cos3x)

1

200

Find the following limits: lim x->3⁺ 1/x-3, lim x->3^- 1/x-3, lim x->3 1/x-3

+OO, -OO, DNE

300

Find the following limit: lim x->1 (x³-1)/(x²-1)

3/2

Composite Functions

100

If f(x)=2x+3, and g(x)=x². Simplify f(g(x)) and f(g(9)).

2x²+3, 165

200

If f(x)=√x+4 and g(x) = 3x²-2. Simplify f(g(x)) and f(g(2)).

√3x²+2, √14

300

If f(x) = 1/x+1 and g(x) = x/2. Simplify f(g(x)) and f(g(3)).

2/x+2, 2/5