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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Example 1

Evaluate the limit.

  • \lim_x\to3x2

Example 2

Evaluate the limit. 

  • \lim_x\to10\sqrtx + 4

Example 3

Evaluate the limit. 

  • \lim_x\to8(x3 + x1/3)

Example 4

Evaluate the limit. 

  • \lim_x\to1(f(x) + 3)2, assuming \lim_x\to1f(x) = 7

Example 5

Evaluate the limit.

  • \lim_x\to1\sqrt7f(x), assuming \lim_x\to1f(x) = 7

Example 6

Find all possible values for the specified limit (we may assume the limit exists).

  • \lim_x\to9f(x), assuming \lim_x\to9(f(x) + x)2 = 81

Example 7

Find all possible values for the specified limit (we may assume the limit exists).

  • \lim_x\to3f(x), assuming \lim_x\to35x(f(x))3 = 45

Example 8

Find all possible values for the specified limit (we may assume the limit exists). 

  • \lim_x\to0f(x), assuming \lim_x\to03\sqrtf(x) = 51

Example 9

Find all possible values for the specified limit (we may assume the limit exists).

  • \lim_x\to12f(x), assuming \lim_x\to12\sqrt2f(x) + 3x = 16

Example 10

Find all possible values for the specified limit (we may assume the limit exists).

  • \lim_x\to2f(x), assuming \lim_x\to2(xf(x))3 = 125
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