Worksheet 8 - Evaluating Limits 8...AP Calculus AB – Worksheet 8 Properties of Limits Once we...
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AP Calculus AB – Worksheet 8 Properties of Limits Once we accept our limits, we go beyond them. – Albert Einstein Evaluate the limit. 1) Plug it in! 2) Factor, then plug in. 3) Graph it or make a table. 1 lim x→−3 3x + 2 ( ) 2 lim x→1 3x 3 − 2 x 2 + 4 ( ) 3 lim x→3 x − 1 x − 4 4 lim x→2 cos π x 3 5 lim x→1 sin π x 2 6 lim x→0 sec 2 x 7 lim x→2 2 − x x 2 − 4 8 lim x→4 x 2 − 5 x + 4 x 2 − 2 x − 8 9 lim x→3 x 2 − 9 x 3 − 27 10 lim x→3 x + 1 − 2 x − 3 11 lim x→0 sin x 5 x 12 lim x→0 31 − cos x ( ) x 13 If lim x→c f x () = 2 and lim x→c gx () = 3 , evaluate each of the following: a) lim x→c 5 gx () ⎡ ⎣ ⎤ ⎦ b) lim x→c f x () + gx () ⎡ ⎣ ⎤ ⎦ c) lim x→c f x () gx () ⎡ ⎣ ⎤ ⎦ d) lim x→c f x () gx () Answers: 1) -7 2) 5 3) − 2 4) − 1 2 5) 1 6) 1 7) − 1 4 8) 1 2 9) 2 9 10) 1 4 11) 1 5 12) 0 13) a) 15 b) 5 c) 6 d) 2 3
Transcript of Worksheet 8 - Evaluating Limits 8...AP Calculus AB – Worksheet 8 Properties of Limits Once we...
AP Calculus AB – Worksheet 8 Properties of Limits Once we accept our limits, we go beyond them. – Albert Einstein Evaluate the limit.
1) Plug it in! 2) Factor, then plug in. 3) Graph it or make a table.
1 lim
x→−33x + 2( )
2 limx→1
3x3 − 2x2 + 4( )
3 limx→3
x −1x − 4
4 limx→2cosπ x
3
5 limx→1sin π x
2
6 limx→0sec2x
7 limx→2
2 − xx2 − 4
8 limx→4
x2 − 5x + 4x2 − 2x − 8
9 limx→3
x2 − 9x3 − 27
10 limx→3
x +1 − 2x − 3
11 limx→0
sin x5x
12 limx→0
3 1− cos x( )x
13 If limx→c
f x( ) = 2 and limx→c
g x( ) = 3 , evaluate each of the following:
a) limx→c
5g x( )⎡⎣ ⎤⎦ b) limx→c
f x( ) + g x( )⎡⎣ ⎤⎦ c) limx→c
f x( )g x( )⎡⎣ ⎤⎦ d) limx→c
f x( )g x( )
Answers: 1) -7 2) 5 3) − 2 4) −
12
5) 1 6) 1
7) −14
8) 12
9) 29
10) 14
11) 15
12) 0 13) a) 15
b) 5 c) 6
d) 23
