Section 1.4 Homework

1. The point  P(9, −3) lies on the curve y = 3/(8 − x).

(a) If Q is the point (x, 3/(8 − x)), use your calculator to find the slope 

of the secant line PQ (correct to six decimal places) for the following values of x.

(i) 8.9

(ii) 8.99

(iii) 8.999

(iv) 8.9999

(v) 9.1

(vi) 9.01

(vii) 9.001

(viii) 9.0001

(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at 
P(9, −3).

(c) Using the slope from part (b), find an equation of the tangent line to the curve at 
P(9, −3).

2. If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by y = 46t − 16

(a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following.

(i) 0.5 seconds

(ii) 0.1 seconds

(iii) 0.05 seconds

(iv) 0.01 seconds

(b) Estimate the instantaneous velocity when t = 2.

3. The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(𝜋t) + 5 cos(𝜋t),
 where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.

(i) [1,2]

(ii) [1,1.1]

(iii) [1,1.01]

(iv) [1,1001]

(b) Estimate the instantaneous velocity of the particle when t = 1.