Find f . f ' ( t ) = sec( t )(sec( t ) + tan( t )),-pi/2 0, f (1) = 0, f (

Findf.

f' (t) = sec(t)(sec(t) + tan(t)),-pi/2f(/4)=3

f(t) =

Findf.

f'' (x) =2 +24x12x²,f(0) =7,f' (0) =12

f(x) =

Findf.

f'' () = sin() + cos(),f(0) =1,f' (0) =3

f()=

Findf.

f'' (x) =10+ 6x+24x²,f(0) =3,f(1) =13

f(x) =

Findf.

f'' (x) =x²,x> 0,f(1) = 0,f(3) = 0

f(x) =

Findf.

f''' (x) = cos(x),f(0) =3,f' (0) =5,f'' (0) =6

f(x) =

Find a functionfsuch thatf'(x) =5x³and the line40x+y= 0 is tangent to the graph off.

f(x) =

A particle is moving with the given data. Find the position of the particle.

v(t) = sin(t)cos(t),s(0) =9

s(t) =

A particle is moving with the given data. Find the position of the particle.

a(t) = 2t+7,s(0) =8,v(0) =8

s(t) =

A particle is moving with the given data. Find the position of the particle.

a(t) =17sin(t) +6cos(t),s(0) = 0,s(2) =14

s(t) =

A stone is dropped from the upper observation deck of a tower,200m above the ground. (Assumeg= 9.8 m/s².)

(a) Find the distance (in meters) of the stone above ground level at timet.

h(t) =

(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)

s

(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)

m/s

(d) If the stone is thrown downward with a speed of8m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

s

A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of38ft/s². What is the distance covered before the car comes to a stop? (Round your answer to one decimal place.)

ft

What constant acceleration is required to increase the speed of a car from21mi/h to52mi/h in4seconds? (Round your answer to two decimal places.)

ft/s²

A car braked with a constant deceleration of16ft/s², producing skid marks measuring50ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

ft/s