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# Evaluating Limits Date Period - limit of piecewise function calculator

Kuta Software - Infinite Calculus Name___________________________________
Evaluating Limits Date________________ Period____
Evaluate each limit.
1) lim
4x + 4
x-1+ x + 1
2) lim f (x), f (x) = {-x - 8, x -1
x-1- -x2 - 4x - 4, x > -1
f(x) f(x)
84
62
4
-8 -6 -4 -2 2 4 6 x
2 -2
-4
-8 -6 -4 -2 2 4 6 x
-2 -6
-4 -8
-6 -10
-8 -12
3) lim f (x), f (x) = {-x2 - 10x - 24, x -3
x -3
2x + 3, x > -3
x, x < -1
4) lim f (x), f (x) = {-x2 + 2x, x -1
x -1
f(x) f(x)
6
4
4
2
2
-10 -8 -6 -4 -2 2 4 x
-2
-8 -6 -4 -2 2 4 6 x
-2
-4
-4
-6
-6
-8
-8
-10
-10
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Evaluate each limit. You may use the provided graph to sketch the function.
5) lim f (x), f (x) = {-x - 3, x -1
x -1-
x + 1, x > -1
-x2 - 4x - 5, x -2
6) lim f (x), f (x) = {-1, x > -2
x -2
f(x) f(x)
66
44
22
-8 -6 -4 -2 2 4 6 x -10 -8 -6 -4 -2 2 4 6 x
-2 -2
-4 -4
-6 -6
-8 -8
Evaluate each limit.
7) lim f (x), f (x) = {1, x 0 x
x0+
-x2 + 4x - 3, x > 0
8) lim
x0- x
9) lim -2x + 1
x0+
x+
9
2 2
, x -2
x -2
2
Critical thinking questions:
13) Give an example of a two-sided limit of a 14) Given an example of a two-sided limit of a
piecewise function where the limit does not function with an absolute value where the limit
exist. does not exist.
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Kuta Software - Infinite Calculus Name___________________________________
Evaluating Limits Date________________ Period____
Evaluate each limit.
1) lim
4x + 4
x-1+ x + 1
2) lim f (x), f (x) = {-x - 8, x -1
x-1- -x2 - 4x - 4, x > -1
f(x) f(x)
84
62
4
-8 -6 -4 -2 2 4 6 x
2 -2
-4
-8 -6 -4 -2 2 4 6 x
-2 -6
-4 -8
-6 -10
-8 -12
4 -7
3) lim f (x), f (x) = {-x2 - 10x - 24, x -3
x -3
2x + 3, x > -3
x, x < -1
4) lim f (x), f (x) = {-x2 + 2x, x -1
x -1
f(x) f(x)
6
4
4
2
2
-10 -8 -6 -4 -2 2 4 x
-2
-8 -6 -4 -2 2 4 6 x
-2
-4
-4
-6
-6
-8
-8
-10
-10
-3 Does not exist.
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How do you find the limit of a function? The limit of the root of a function equals the corresponding root of the limit of the function. One way to find the limit of a function expressed as a quotient is to write the quotient in factored form and simplify. See Example. Another method of finding the limit of a complex fraction is to find the LCD. See Example.

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