MAT Review for Calc Unit 1

Use the graph of f(x) below to find the following limit.

-1

0

1

dne

lim

x→1+

f(x) =

Use the graph of f(x) below to find the following limit.

-1

0

1

dne

lim

x→1-

f(x) =

Use the graph of f(x) below to find the following limit.

-1

0

1

dne

lim

x→1

f(x) =

Use the graph of f(x) below to find the following limit.

0

+∞

-∞

dne

lim

x→4+

f(x) =

Use the graph of f(x) below to find the following limit.

0

+∞

-∞

dne

lim

x→3

f(x) =

Identify the type of discontinuity and where it

occurs for the following function.

jump at x = 3

point at x = 3

infinite at x = 3

continuous

f(x) =
  4
x - 3

Identify the type of discontinuity and where it

occurs for the following function.

jump at x = -2

point at x = -2

infinite at x = -2

continuous

f(x) = 3x + 6

Identify the type of discontinuity and where it

occurs for the following function.

infinite at x = 3, point at x = 2

infinite at x = 2, point at x = 3

infinite at x = 3, infinite at x = 2

point at x = 2, point at x = 3

f(x) =
      x - 2
x2 - 5x + 6

Identify the type of discontinuity and where it

occurs for the following function.

cont. when x ≤ -5/3

cont. when x ≥ -5/3

cont. when x = -5/3

continuous

f(x) = √3x + 5

Identify the type of discontinuity and where it

occurs for the following function.

cont. when x ≤ 7/4

cont. when x ≥ 7/4

cont. when x = 7/4

continuous

f(x) = √4x - 7
3
Find the average rate of change over the given interval.
f(x) = 4x - 5      [2, 4]

1/4

3

4

12

Find the average rate of change over the given interval.
f(x) = 3x2 - 2x +1      [-2, 3]

-5

-1

1

5

Find the limit h→0 of the average rate of

change of f(x) = x2 - 2x - 5 at x = 4.

6

8

10

19

Find the slope of the line tangent to the curve

              f(x) = x3 - 4x + 2 at x = 2.

3

8

10

Find the limit of the following problem.

-7

+∞

-∞

does not exist

lim
x→-3
x + 3
x - 4
Find the limit of the following problem.
x→-2+
lim

-5

 5

+∞

does not exist

(x + 7)
x + 2
x + 2
Find the limit of the following problem.
x→3-
lim

-22

 -8

8

9

{
2x + 3 if x ≥ 3
5x - 7 if x ≤ 3

Find the equation of the line tangent to the curve.

y - 3 = 12(x - 7)

y - 3 = 4(x - 7)

y - 7 = 12(x - 3)

y - 7 = 4(x - 3)

f(x) = 4x + 9 at (3, 7)

Find the equation of the line normal to the curve.

y - 4 = 7(x - 2)

y - 4 = -7(x - 2)

y - 4 = 1/7(x - 2)

y - 4 = -1/7(x - 2)

f(x) = 3x2 - 5x at (2, 4)

Find the equation of the line tangent to the curve.

y + 1 = 11(x - 2)

y + 1 = -13(x - 2)

y - 1 = 11(x + 2)

y - 1 = -13(x + 2)

f(x) = x3 - x + 5 at (-2, 1)
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