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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Example 1

Given that

\lim_x\to12f(x) = 7,

evaluate the following limit.

Example 2

Given that

\lim_x\to12f(x) = 7,

evaluate the following limit.

Example 3

Given that

\lim_x\to12f(x) = 7,

evaluate the following limit.

\lim_x\to12(10-2f(x))

Example 4

Given that

\lim_x\to12f(x) = 7,

evaluate the following limit.

\lim_x\to12(f(x) + 3x-1)

Example 5

Given that

\lim_x\to12f(x) = 7,

evaluate the following limit.

\lim_x\to1210f(x)-\lim_x\to12(3 + 5f(x))

Example 6

Assuming that \lim_x\to4f(x) exists, find this limit if

\lim_x\to420f(x) = 100

Example 7

Assuming that \lim_x\to4f(x) exists, find this limit if

 \lim_x\to4(5f(x) + 11) = 26

Example 8

Assuming that \lim_x\to4f(x) exists, find this limit if 

 \lim_x\to4(6x-2f(x)) = 26

Example 9

Assuming that \lim_x\to4f(x) exists, find this limit if 

 \lim_x\to4(2-3x + 10f(x)) = 0

Example 10

Assuming that \lim_x\to4f(x) exists, find this limit if

\lim_x\to4(2f(x) + x)-\lim_x\to4(f(x)-x) = 10

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