3.2 Additional Practice Problems PDF

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Download 3.2 Additional Practice Problems PDF

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3.2 Additional Practice Problems Here are some additional problems for those of you who want more practice with the terms and calculations we did in the 3.2 notes. These practice problems are not graded, so don’t feel like you have to do them if you feel comfortable enough with the 3.2 material. An answer key will be posted shortly!

Example 1 Evaluate the following limit. 𝑥 𝑥→∞ 𝑒 𝑥 lim

Example 2 (from Briggs, Cochran, & Gillett, 2011, pg. 245) Evaluate the following limit. 1 − cos(6𝑥) 𝑥→0 2𝑥 lim

Example 3 (from Briggs, Cochran, & Gillett, 2011, pg. 249) Evaluate the following limit. lim 2𝑡 cot 𝑡 𝑡→0

Example 4 (from Briggs, Cochran, & Gillett, 2011, pg. 236) Evaluate the following limit. lim𝜋 𝑥→

2

1 + tan 𝑥 sec 𝑥

Example 5 (from Briggs, Cochran, & Gillett, 2011, pg. 238) Evaluate the following limit. 3 sin(4𝑥) 𝑥→0 5𝑥 lim

Example 6 Evaluate the following limit. √9 − 3𝑥 − 3 𝑥→0 𝑥 lim

Example 7 Evaluate the following limit. 𝑡

lim √𝑡 4

𝑡→∞

Example 8 Evaluate the following limit. 𝑥 3 − 2𝑥 + 1 𝑥→∞ 𝑥3 lim

Example 9 (from Briggs, Cochran, & Gillett, 2011, pg. 239) Evaluate the following limit. lim− (1 − 𝑥) tan (

𝑥→1

𝜋𝑥 ) 2

Example 10 Evaluate the following limit. sec 𝑡 − 1 𝑡→0 𝑡2 lim

Example 11 Evaluate the following limit. lim𝜋 𝜃→ 2

(tan 𝜃)cos 𝜃

Example 12 (from Briggs, Cochran, & Gillett, 2011, pg. 236) Evaluate the following limit. lim 𝑥 2 sin (

𝑥→∞

1 ) 4𝑥 2...