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please solve the entire problem as required with all neccesery steps.

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please solve the entire problem as required with all neccesery steps.

Math 210: Written Homework 1, due Monday February 11th
Name:________________________
Instructions: Write all explanations neatly. Use proper mathematical notation. Part of your grade will
be based on quality of writing.
1) (30 pts) For parts a – d, evaluate the limit.
a. (8) Compute this limit. You may use either method shown in class.
lim
−3𝑥 2 −5𝑥
𝑥→−∞ 𝑥 2 +7𝑥+10
1
b. (6) lim ( 𝑥 + 𝑒 𝑥 )
𝑥→−∞
2𝑥 2 + 5,𝑥 < 0
c. (8) 𝑓(𝑥) = { 3−5𝑥3
,𝑥 ≥ 0
1+4𝑥+𝑥3
i. lim 𝑓(𝑥)
𝑥→∞
ii. lim 𝑓(𝑥)
𝑥→−∞
d. (8) Use the Squeeze Theorem to compute the limit. SHOW ALL YOUR STEPS.
(cos 𝑥)+2
𝑥3
lim
𝑥→∞
2) (10 pts) Given the function, find the value of 𝑘 that makes the function continuous everywhere.
𝑓(𝑥) = {
7𝑥 − 2,𝑥 ≤ 1
𝑘𝑥 2 ,
𝑥>1
3) (10 pts) On one graph, sketch the function with these given properties. You do not need to find a
formula for the function. If there is a vertical asymptote, state its equation. If there is a horizontal
asymptote, state its equation.
1
𝑓(1) = 0
𝑓(0) = − 2
lim − 𝑓(𝑥) = −∞
lim + 𝑓(𝑥) = ∞
𝑥→−2
𝑥→−2
𝑓(4) = 3
lim 𝑓(𝑥) = 1
𝑥→−∞

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Anonymous

I was struggling with this subject, and this helped me a ton!