EVALUATING LIMITS ALGEBRAICALLY WORKSHEET

Evaluate the following limits without using a calculator.

Problem 1 :

lim x → 3 2x2 - 5x - 3x - 3

Solution

Problem 2 :

lim x → 2 x4 - 16x - 2

Solution

Problem 3 :

lim x → -1 x4 + 3x3 - x2 + x + 4x + 1

Solution

Problem 4 :

lim x → 0 x + 4 - 2x

Solution

Problem 5 :

lim x → 3 x + 6 - xx - 3

Solution

Problem 6 :

lim x → -2 12 + 1xx + 2

Solution

Problem 7 :

lim x → 12 x-1 - 2x - 12

Solution

Problem 8 :

lim x → 3 1x2 - 19x - 3

Solution

Problem 9 :

lim x → 0 5x2 + x - 5x

Solution

Answer Key

1)  7

2)  32

3)  8

4)  1/4

5)  -5/6

6) -1/4

7)  -4

8)  -2/27

9)  -5

No calculator is allowed. Evaluate each limit algebraically.

Problem 1 :

x→03x+5

Solution

Problem 2 :

x→52-3x

Solution

Problem 3 :

x→88-x

Solution

Problem 4 :

x→3x+2x

Solution

Problem 5 :

x→0x+2x

Solution

Problem 6 :

x→4x2-16x-4

Solution

Problem 7 :

x→2x3-82-x

Solution

Problem 8 :

x→2x2+2x-8x-2

Solution

Problem 9 :

x→42x2-5x-12x-4

Solution

Problem 10 :

x→-5x+5x3+125

Solution

Problem 11 :

x→3x3-3x2-4x+12x-3

Solution

Answer Key

1)  5

2)  -13

3)  0

4)  5/3

5)  undefined

6)  8

7)  -12

8)  6

9)  11

10)  1/75

11)  5

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