Math 103. Homework 4. Due 2/27/02

1. Find the limits, if they exist.

(a)




lim x® ¥  x3+2x+1 1-4x3


(b)




lim x® -¥  x-1 2x3+x+2

2.[84, p. 133] The concentration of a certain drug in a patient's bloodstream t hours after injection is given by

C(t) = (0.2) t t2+1

mg/cm³. Evaluate lim_{t® ¥} C(t) and interpret your result.

3.[42, p. 146] Find the one-sided limits lim_{x® 1+} f(x) and lim_{x® 1-}f(x), if they exist, where f(x) is given by

f(x) = ì ï ï í ï ï î x+2   ___ Öx-1   if x ³ 1, 1-   ___ Ö1-x   if x < 1

4.[62, p. 147] Find the values of x for which the following function is continuous

f(x)= ì í î x+1 if x £ 1, 1-x2 if x > 1

5.[92, p. 154] Joan is looking straight out of a window of an apartment building at a height of 32 ft from the ground. A boy throws a tennis ball straight up by the side of the building where the window is located. The height of the ball (in feet) from the ground at time t is h(t) = 4+64 t - 16 t².

(a) Show that h(0)=4 and h(2)=68 and then use the intermediate value theorem to conclude that the ball must cross Joan's line of sight at least once.
(b) At what time(s) does the ball cross Joan's line of sight? (Hint. You have to solve a quadratic equation.)

Suggested Problems Section 2.4.- Odds 31-89. Section 2.5.- Odds 1-97.