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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Example 1

Find the following limit, assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32.

  •  \lim_x\to10(f(x)g(x))

Example 2

Find the following limit, assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32.

  •  \lim_x\to10(4xf(x)g(x))

Example 3

Find the following limit, assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32.

  • \lim_x\to10(xf(x) + 20)

Example 4

Find the following limit, assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32.

  • \lim_x\to10(x-g(x)\cdot g(x))

Example 5

Find the following limit, assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32.

\item \lim_x\to10(x2g(x) + f(x))

Example 6

Assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32,
find the following limits.

  • \lim_x\to10(\fracf(x)g(x))

Example 7

Assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32,
find the following limits.

  • \lim_x\to10(\frac1f(x))

Example 8

Assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32,
find the following limits.

  • \lim_x\to10(\fracf(x) + 2g(x)x-2)

Example 9

Assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32,
find the following limits.

  • \lim_x\to10(\fracx-3f(x)5)

Example 10

Assuming that
\lim_x\to10f(x) = 5 and \lim_x\to10g(x) = \frac32,
find the following limits.

  • \lim_x\to10(\fracx-2f(x)g(x))

Example 11

Find \lim_x\to5f(x) (we may assume this limit exists).

  •  \lim_x\to5(\fracf(x)x-2) = 2

Example 12


Find \lim_x\to5f(x) (we may assume this limit exists).

  •  \lim_x\to5(2xf(x)) = 20

Example 13

Find \lim_x\to5f(x) (we may assume this limit exists).

  • \lim_x\to5(f(x))2 = 16

Example 14

Find \lim_x\to5f(x) (we may assume this limit exists).

  • \lim_x\to5(\frac14x-f(x)) = \frac12

Example 15

Find \lim_x\to5f(x) (we may assume this limit exists).

  • \lim_x\to5(\frac\frac14x + f(x)4f(x)) = \frac32
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