# AMC Calculus Worksheet

• January 31, 2022/

### Description

Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

(a)lim x → 2f(x)

(b)

lim x → 2+f(x)

(c)

lim x → 2 f(x)

(d)

f(2)

(e)

lim x → 4 f(x)

(f)

f(4)

For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

(a)lim x → −3h(x)

(b)

lim x → −3+h(x)

(c)

lim x → −3 h(x)

(d)

h(−3)

(e)

lim x → 0h(x)

(f)

lim x → 0+h(x)

(g)

lim x → 0 h(x)

(h)

h(0)

(i)

lim x → 2 h(x)

(j)

h(2)

(k)

lim x → 5+h(x)

(l)

lim x → 5h(x)

3.

For the function g whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

(a)lim t → 0g(t)

(b)

lim t → 0+g(t)

(c)

lim t → 0 g(t)

(d)

lim t → 2g(t)

(e)

lim t → 2+g(t)

(f)

lim t → 2 g(t)

(g)

g(2)

(h)

lim t → 4 g(t)

#### 4.

Sketch the graph of the function.f(x) =

 3 + x if x < −1 x2 if −1 ≤ x < 1 2 − x if x ≥ 1

Use the graph to determine the values of a for which

lim xa f(x)

a =

#### 6.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.lim x0

 tan(4x) tan(5x)

#### 7.

[–/9 Points]SCALCET8 2.2.009.

For the function f whose graph is shown, state the following. (If an answer does not exist, enter DNE.)

(a)lim x → −7 f(x)

(b)

lim x → −3 f(x)

(c)

lim x → 0 f(x)

(d)

lim x → 6f(x)

(e)

lim x → 6+f(x)

(f) The equations of the vertical asymptotes.

 x = (smallest value) x = x = x = (largest value)