Chapter 2 | Limits
133
by s ( t ) =200−4.9 t 2 , where position s is measured in meters and time t is measured in seconds. Round your answer to eight significant digits. 16. [T] Compute the average velocity of the ball over the given time intervals. a. ⎡ ⎣ 4.99, 5 ⎤ ⎦
10. [T] Complete the following table with the appropriate values: y -coordinate of Q , the point Q ( φ , y ), and the slope of the secant line passing through points P and Q . Round your answer to eight significant digits. x y Q ⎛ ⎝ ϕ , y ⎞ ⎠ m sec
1.4
a.
e.
i.
b. ⎡ c. ⎡ d. ⎡
⎣ 5, 5.01 ⎤ ⎦ ⎣ 4.999, 5 ⎤ ⎦ ⎣ 5, 5.001 ⎤ ⎦
1.49
b.
f.
j.
17. Use the preceding exercise to guess the instantaneous velocity of the ball at t =5 sec. For the following exercises, consider a stone tossed into the air from ground level with an initial velocity of 15 m/sec. Its height in meters at time t seconds is h ( t ) =15 t −4.9 t 2 . 18. [T] Compute the average velocity of the stone over the given time intervals. a. ⎡ ⎣ 1, 1.05
1.499
c.
g.
k.
1.4999 d.
h.
l.
11. Use the values in the right column of the table in the preceding exercise to guess the value of the slope of the tangent line to f at φ =1.5. 12. Use the value in the preceding exercise to find the equation of the tangent line at point P . For the following exercises, points P (−1, −1) and Q ( x , y ) are on the graph of the function f ( x ) = 1 x . 13. [T] Complete the following table with the appropriate values: y -coordinate of Q , thepoint Q ( x , y ), and the slope of the secant line passing through points P and Q . Round your answer to eight significant digits. x y Q ( x , y ) m sec
⎤ ⎦ b. [1, 1.01] c. ⎡ ⎣ 1, 1.005 ⎤ ⎦ d. [1, 1.001]
19. Use the preceding exercise to guess the instantaneous velocity of the stone at t =1 sec. For the following exercises, consider a rocket shot into the air that then returns to Earth. The height of the rocket in meters is given by h ( t ) = 600 + 78.4 t −4.9 t 2 , where t is measured in seconds. 20. [T] Compute the average velocity of the rocket over the given time intervals.
−1.05
a.
e.
i.
a. [9, 9.01] b. [8.99, 9] c. [9, 9.001] d. [8.999, 9]
−1.01
b.
f.
j.
−1.005 c.
g.
k.
21. Use the preceding exercise to guess the instantaneous velocity of the rocket at t =9 sec. For the following exercises, consider an athlete running a 40-m dash. The position of the athlete is given by d ( t ) = t 3 6 +4 t , where d is the position in meters and t is the time elapsed, measured in seconds.
−1.001 d.
h.
l.
14. Use the values in the right column of the table in the preceding exercise to guess the value of the slope of the line tangent to f at x =−1. 15. Use the value in the preceding exercise to find the equation of the tangent line at point P . For the following exercises, the position function of a ball dropped from the top of a 200-meter tall building is given
Made with FlippingBook - professional solution for displaying marketing and sales documents online