代写Math 3A Practice Problems #3 Summer 2024代做留学生SQL语言

Math 3A

Practice Problems #3

Summer 2024

1. Given the position function  where t is in seconds and s is in feet, find the following:

A. the velocity and acceleration function

B. when the particle is at rest

C. the total distance traveled during the first 6 seconds

D. when the particle is speeding up and slowing down

2. A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 5 ft above the ground?

3. Use a local linear approximation to estimate (you should not need to use a calculator):

4. Find the derivative (simplify if possible): f (x) = cosh(ln 5x)

5. The side of a cube is measured to be 25 cm, with a possible error of 0.5 cm.

A. Use differentials to estimate the error in the volume.

B. Estimate the percentage errors in the side and volume.

6. Grain pouring from a chute at the rate of 8 ft3 /min forms a conical pile whose height is always twice its radius. How fast is the height of the pile increasing at the instant when the pile is 6 ft high?