School

Ball State UniversityDepartment

Mathematical SciencesCourse Code

MATH 165Professor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**1 pages of the document.**Maths 165

Review Sheet 3

Answers

1. 9.99

2. 9.99

4. y=xis a slant asymptote (as x→ −∞)

5. When x= 1,000/3, then P(x) = ...

6. 2.68269579

7. 1.01395761

8. −16

5

9. (a) -1

2

(b) 2

(c) 2

(d) e−1/2

10. (a) Absolute max = 7. Absolute min

=−9.

(b) Abs. max = 4e2. Abs. min = 0.

(c) Abs. max 0. Abs. min = −6.

11. f′(x) = 0 at x=1

3and f′(x) d.n.e. at

x= 0.

12. 4 ≤f(4) ≤16.

13. It does not contradict the Mean Value

Theorem!

14. (a) Increasing on (−∞,1

3)∪(1,∞) and

decreasing on (1

3,1). Local max at x=1

3. Local

min at x= 1.

(b) Increasing on (−2,2

5) and decreasing on

(−∞,−2) ∪(2

5,∞). Local min at x=−2, Local

max at x=2

5.

(c) Decreasing on (−∞,0) and increasing on

(0,∞). Local min at x= 0.

(d) Increasing on (−π, −π

2)∪(0,π

2) and

decreasing on (−π

2,0) ∪(π

2, π). Local max at

x=±π

2and local min at x= 0.

15. It is always concave up. No inﬂection

points!

16. About 2.33 hours.

17. 2.

18. f(x) = 3ex−5 sin(x) + 4x−2.

19. (a) v(t) = 80 −40tand x(t) = 80t−20t2.

(b) No.

20. (a) p(t) = 100e³−tln 2

1.4×10−4´

(b) p(4.3×10−4) = 100e³−(4.3) ln 2

1.4´≈11.896 mg

###### You're Reading a Preview

Unlock to view full version