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

a. Find the average velocity for the time period beginning when t = 2 and lasting

(i) 0.5 second. Answer: -26

(ii) 0.1 second. Answer: -19.6

(iii) 0.05 second. Answer: -18.8

(iv) 0.01 second. Answer: -18.16

b. Estimate the instantaneous velocity when t = 2.

Answer: -18

If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given by y = 48t -16t^2.

c. Find the average velocity for the time period beginning when t = 2 and lasting

(v) 0.5 second. Answer: -24

(vi) 0.1 second. Answer: -17.6

(vii) 0.05 second. Answer: -16.8

(viii) 0.01 second. Answer: -16.16

d. Estimate the instantaneous velocity when t = 2.

Answer: -16

If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given by y = 50t -16t^2.

e. Find the average velocity for the time period beginning when t = 2 and lasting

(ix) 0.5 second. Answer: -22

(x) 0.1 second. Answer: -15.6

(xi) 0.05 second. Answer: -14.8

(xii) 0.01 second. Answer: -14.16

f. Estimate the instantaneous velocity when t = 2.

Answer: -14

Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

2. (a) Answer: 3

(b) Answer: 1

(c) Answer: DNE

(e) Answer: 4

(f) Answer: DNE

For the function g whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

3. (a) Answer: -1

(b) Answer: -2

(c) Answer: DNE

(e) Answer: 2

(f) Answer: DNE

(g) Answer: 1

(h) Answer: 3

4. If an arrow is shot upward on the moon with a speed of 64m/s its height in meters t seconds later is given by y = 64t – 0.83t^2 (Round your answer to two decimal places.)

(a) Find the average speed over the given time intervals.

(i) Answer: 61.51

(ii) Answer: 61.93

(iii) Answer: 62.26

(iv) Answer: 62.33

(v) Answer: 62.34

(b) Estimate the speed when t = 1

Answer: 62.34

If an arrow is shot upward on the moon with a speed of 68m/s its height in meters t seconds later is given by y = 68t – 0.83t^2 (Round your answer to two decimal places.)

(c) Find the average speed over the given time intervals.

(vi) Answer: 65.51

(vii) Answer: 65.93

(viii) Answer: 66.26

(ix) Answer: 66.33

(x) Answer: 66.34

(d) Estimate the speed when t = 1

Answer: 66.34

5. Evaluate the function f(x) at the given numbers(correct to six decimal places).

f(x) = (x^2-3x)/(x^2-2x-3), x = 0,-0.5,-0.9,-0.95,-0.99,-0.999,-2,-1.5,-1.01,-1.001

f(0) = 0

f(-0.5) = -1

f(-0.9) = -9

f(-0.95) = -19

f(-0.99) = -99

f(-0.999) = -999

f(-2) = 2

f(-1.5) = 3

f(-1.1) = 11

f(-1.01) =101

f(-1.001) = 1001

Guess the value of the limit of f(x) as x approaches -1, correct to six decimal places. (If an answer does not exist, enter DNE.)

lim x approaches -1 [(x^2-3x)/(x^2-2x-3)] = DNE

**All answers are the same for this problem even with different red numbers. **

6. Use a table of values to estimate the value of the limit. If you have a graphing device use is to confirm your results graphically. (Round your answer to two decimal places.)

Lim x approaches 0 ((sqrt(x+49)-7))/x

Answer: 0.07

Use a table of values to estimate the value of the limit. If you have a graphing device use is to confirm your results graphically. (Round your answer to two decimal places.)

Lim x approaches 0 ((sqrt(x+64)-8))/x

Answer: 0.06

7. Use a table of values to estimate the value of the limits. If you have a graphing device, use it to confirm your results graphically. (Round your answer to two decimal places.)

lim x approaches 1 (x^7-1)/(x^5-1)

Answer: 1.40

Use a table of values to estimate the value of the limits. If you have a graphing device, use it to confirm your results graphically. (Round your answer to two decimal places.)

lim x approaches 1 (x^9-1)/(x^5-1)

Answer: 1.8

Use a table of values to estimate the value of the limits. If you have a graphing device, use it to confirm your results graphically. (Round your answer to two decimal places.)

lim x approaches 1 (x^8-1)/(x^4-1)

Answer: 2