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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Example 1

Find the limit.

Picture

  • \lim_x\to -1^-f(x)

Example 2

Find the limit.

PICTURE

  •  \lim_x\to -1^ + f(x)

Example 3

Find the limit.

PICTURE

  • \lim_x\to 0^-f(x)

Example 4


Find the limit.

PICTURE

  •  \lim_x\to 0^ + f(x)

Example 5

For the function f(x) and specified value of a, find the left-side and right-side limits of f(x) as x approaches a.
Determine if \lim_x\to af(x) exists, and if so state its value.



  • a = 5, f(x) =
    lr
    7x + 1&x ≠ 5
    29&x > 5.

Example 6

For the function f(x) and specified value of a, find the left-side and right-side limits of f(x) as x approaches a.
Determine if \lim_x\to af(x) exists, and if so state its value.



  • a = 0, f(x) = |x|

Example 7

For the function f(x) and specified value of a, find the left-side and right-side limits of f(x) as x approaches a.
Determine if \lim_x\to af(x) exists, and if so state its value.

\item

a = 3, f(x) =
lr
3x-3&x ≤ 3
3x + 3&x > 3.

Example 8

For the function f(x) and specified value of a, find the left-side and right-side limits of f(x) as x approaches a.
Determine if \lim_x\to af(x) exists, and if so state its value.

\item

a = -10, f(x) =
lr
3&x ≤ 4
0&x > 4.

Example 9

For the function f(x) and specified value of a, find the left-side and right-side limits of f(x) as x approaches a.
Determine if \lim_x\to af(x) exists, and if so state its value.

\item

a = 1,
f(x) =
lr
x + 1 &x < 1
0 x = 1
4-2x &x >1.

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