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Topics

Introduction to Functions, Graphs, And Limits - At A Glance:

Power Property

If  exists, and p is any real number,

Sample Problem

If   then

Example 1

Find \lim_x\to4f(x), assuming this limit exists and that \lim_x\to44(f(x))2 = 100.


Example 2

Find \lim_x\to3f(x), 

 assuming this limit exists and that \lim_x\to3((f(x))^1/4 + x) = 7.


Example 3

Find \lim_x\to5f(x),

assuming this limit exists and that \lim_x\to5(x2\sqrtf(x)) = 5.


Exercise 1

Evaluate the limit.

  • \lim_x\to3x2

Exercise 2

Evaluate the limit. 

  • \lim_x\to10\sqrtx + 4

Exercise 3

Evaluate the limit. 

  • \lim_x\to8(x3 + x1/3)

Exercise 4

Evaluate the limit. 

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

Exercise 5

Evaluate the limit.

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

Exercise 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

Exercise 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

Exercise 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

Exercise 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

Exercise 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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