MAT 265 Exam 2 Review | Arizona State University, Tempe

MAT 265 Exam Two Review Sections: 2.4-2.8, 3.1-3.3, 3.5, 3.7
Correct Answer is highlighted red - 39 questions
Rules
Section 2.4

1. Use the following table to answer question 1.
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𝑥 𝑓(𝑥) 𝑔(𝑥) 𝑓 ′ (𝑥) 𝑔′ (𝑥)
1 4 3 2 1
2 3 4 3 4
3 2 1 4 2

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4 1 2 1 3
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If 𝐻(𝑥) = 𝑓(𝑥) ∙ 𝑔(𝑥), what is 𝐻′(2)? 24
24 fizi.giydx

2. Given 𝑓(𝑥) = 5 csc 𝑥, find a) 𝑓′(𝑥) b) 𝑓′′(𝑥). fi iiii amn
𝑓 ′ (𝑥) = −5 csc 𝑥 cot 𝑥; 𝑓 ′′ (𝑥) = −5(csc 𝑥 − 2 csc 3 𝑥)
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3. The equation of motion for a particle is 𝑠(𝑡) = 5 cos 𝑡 + 6 sin 𝑡 , 𝑡 ≥ 0 , where s is measured in
centimeters and t in seconds. Find the velocity function.
𝑠 ′ (𝑡) = −5 sin 𝑡 + 6 cos 𝑡 5211 5sint 6cost

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4. Find the derivative. 𝑓(𝑥) = 𝑥10 cos 𝑥
𝑓 ′ (𝑥) = 10𝑥 9 cos 𝑥 − 𝑥10 sin 𝑥
fix 101cost x's.mx
10xicosxxos.mx

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5. Find 𝑓′(𝑥) if 𝑓(𝑥) = 4𝑥(sin(𝑥) + cos(𝑥)) fix 4 sinxcosx Yx costsinx
𝑓′(𝑥) = 4(sin(𝑥) + cos (𝑥)) + 4x(cos(𝑥) − sin (𝑥))


6. An object with weight P is dragged along a horizontal plane by a force acting along a rope
attached to the object. If the rope makes an angle t with the plane, then the magnitude of the force is
cP
F= , where c is a constant called the coefficient of friction. Let P = 30 lb and c = 0.5.
c sint+cost
When (in radians) is the rate of change of F with respect to t equal to zero?
arctan 0.5

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, MAT 265 – Calculus for Engineers-I EXAM # 2 Review



Section 2.5

7. Find the first derivative of 𝑦 = tan4 𝑥. 4tank seek
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𝑦 ′ = 4 tan3 𝑥 sec 2 𝑥
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8. Find the equation of the tangent line for 𝑦 = cos 3 (𝑥) at 𝑥 = 0.

𝑦 = 1. me To 315101 0
16 yto 6
Use the following table to answer question questions # 9 and # 10.
𝑥 𝑓(𝑥) 𝑔(𝑥) 𝑓 ′ (𝑥) 𝑔′ (𝑥)
1 2 1 3 2 g
2 2 2 1 3
3 3 1 3 1
flight Rule
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9. If ℎ(𝑥) = 𝑓(𝑔(𝑥)), what is ℎ′(1)? b 1 ftp.fc2 dygt flgexsl.ge
6 h e Figle glx 3
10. If 𝐻(𝑥) = 𝑔(𝑓(𝑥)), what is 𝐻′(3)? Hessiities
3 it4x 13 3
H x g fix fix since
11. Find the 28th derivative of 𝑦 = cos(4𝑥). yes
yes y coscyx
𝑦 (28) = 428 cos(4𝑥)

12. Find the derivative.
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𝑦 = (sec(𝑥))4 + cos (𝑥 5 )
Ysecrecytanx Smes 5 41
4sec
xtanx 5 4sin xs
𝑦 ′ = 4(sec(𝑥))4 tan(𝑥) − 5𝑥 4 sin (𝑥 5 )
3𝑥
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13. Suppose that 𝑓(𝑥) = (2−4𝑥)4. Find the equation of the tangent line of 𝑓 at 𝑥 = 1.
Round each numerical value to 4 decimal places.
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fix 3 24 teuxicust.sce.my
1
𝑦 = −1.3125𝑥 + 1.5


14. If 1000 dollars is invested at an annual interest rate 𝑟 compounded monthly, the amount in the
account at the end of 4 years is given by

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1 48
𝐴 = 1000 (1 + 𝑟) in
12

Find the rate of change of the amount A with respect to the rate r when 𝑟 = 4%

4677.204 A 48000 1 1112 11121

4800011 1220.0415211121
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© School of Mathematical & Statistical Sciences – Arizona State University 48000 1.1693 1 4677.2
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