# 6 calc questions

calculus multi-part question and need the explanation and answer to help me learn.

Requirements: answer and follow instructions on decimals

Points

P(1, 2)

and

Q(x, y)

are on the graph of the function

f(x) = x2 + 1.

Complete the table with the appropriate values of the y-coordinate of Q, the point

Q(x, y),

and the slope of the secant line passing through points P and Q. (Round your answers to seven decimal places.)

Use the values in the right column of the table to guess the value of the slope of the line tangent to f at

x = 1.

Use the value from the question above to find the equation of the tangent line at point P.

y =

Graph

f(x)

and the tangent line.

Points

P(4, 2)

and

Q(x, y)

are on the graph of the function

f(x) =

.

Complete the table with the appropriate values of the y-coordinate of Q, the point

Q(x, y),

and the slope of the secant line passing through points P and Q. (Round your answers to seven decimal places.)

Use the values in the right column of the table to guess the value of the slope of the tangent line to f at

x = 4.

Use the value from the question above to find the equation of the tangent line at point P.

y =

3.

Points

P(−1, −1)

and

Q(x, y)

are on the graph of the function

f(x) =

.

Complete the table with the appropriate values of the y-coordinate of Q, the point

Q(x, y),

and the slope of the secant line passing through points P and Q. (Round your answers to seven decimal places.)

Use the values in the right column of the table to guess the value of the slope of the tangent line to f at

x = −1.

Use the value from the question above to find the equation of the tangent line at point P.

y =

4.

The position function of a ball dropped from the top of a 180 meter tall building is given by

s(t) = 180 − 4.9t2,

where position s is measured in meters and time t is measured in seconds.

Compute the average velocity (in m/s) of the ball over the given time intervals. (Round your answers to six decimal places.)

[4.99, 5]

m/s

[5, 5.01]

m/s

[4.999, 5]

m/s

[5, 5.001]

m/s

Consider the average velocities above to guess the instantaneous velocity (in m/s) of the ball at

t = 5 s.

(Round your answer to the nearest integer.)

m/s

Consider a stone tossed into the air from ground level with an initial velocity of 16 m/s. Its height in meters at time t seconds is

h(t) = 16t − 4.9t2.

Compute the average velocity (in m/s) of the stone over the given time intervals. (Round your answers to six decimal places.)

[1, 1.05] m/s[1, 1.01] m/s[1, 1.005] m/s[1, 1.001] m/s

Consider the average velocities above to guess the instantaneous velocity (in m/s) of the stone at

t = 1 s.

(Round your answer to one decimal place.)

m/s

Consider an athlete running a 40 m dash. The position of the athlete is given by the following equation, where d is the position in meters and t is the time elapsed, measured in seconds.

d(t) =

+ 6t

(a)

Compute the average velocity (in m/s) of the runner over the given time intervals. (Round your answers to seven decimal places.)

(i)

[1.95, 2.05]

m/s

(ii)

[1.995, 2.005]

m/s

(iii)

[1.9995, 2.0005]

m/s

(iv)

[1.99999, 2.00001]

m/s

(b)

Use part (a) to guess the instantaneous velocity (in m/s) of the runner at

t = 2

seconds. (Round your answer to the nearest whole number.)

m/s