calculus

Math E-15 Homework 2
1. Find all solutions x for each equation below. Give both exact answers and approximations correct to three decimal places.
(a) 3ex = 12(72x) (b) lnx=2
(c) x3ex 6xex = 0
2. The radioactive element iodine-131 is commonly used in treating medical problems. It has a half-life of 8.1 days. How long does it take for 99% of a sample of iodine-131 to decay? Give both an exact answer and an approximation correct to three decimal places.
3. If an investment grows exponentially and doubles every 10 years, how long will it take to triple? Give both an exact answer and an approximation correct to three decimal places.
4. Evaluate the following limits.
(a) (b) (c)
lim 3
x x2
lim 53
x
lim (62x)
x
5. On a particular day, a towns electricity usage can be approximated by a sinusoidal function U(t), where t = 0 corresponds to midnight. The function has a period of 24 hours and goes from a low of 30,000 kilowatts at 6 a.m. to a high of 60,000 kilowatts at 6 p.m. Write a formula for U (t), where t is measured in hours.
6. Simplify cos(arcsin x) by rewriting it as an expression that contains no trigonometric or inverse trigono- metric functions. Please draw a triangle as part of showing your work.