Calculus Answers

1. A ladder 15 ft long rests against a vertical wall. Its top slides down the wall
while its bottom moves away along the level ground at a speed of 2 ft/s. How
fast is the angle between the top of the ladder and the wall changing when the
angle is p/3 radians?

2. A ladder 12 meters long leans against a wall. The foot of the ladder is pulled
away from the wall at the rate 12 m/min. At what rate is the top of the ladder
falling when the foot of the ladder is 4 meters from the wall?

3. A rocket R is launched vertically and its tracked from a radar station S which
is 4 miles away from the launch site at the same height above sea level.
At a certain instant after launch, R is 5 miles away from S and the distance
from R to S is increasing at a rate of 3600 miles per hour. Compute the
vertical speed v of the rocket at this instant.

The expression I = 6t^3 + 2t^2 + 5t - 2 shows the relationship between current and time in seconds. How would you find the electric charge passing between t = 2s and t = 5s.

when there is the equation W = 200.Sin(10πt) find out he work done take into consideration that compression takes place only in the first half cycle. t = 0 to t = 0.1 s)

I was wondering when the relationship of a capacitor in voltage and time is given by V = 95(1-e^-0.1t )

how would the graph look when you plot the graph between t = 0 and t = 50 at 10 intervals.
Also Find the differentiation value at t = 10.to verify your solution use calculus.

1. Sketch the graph of the following condition:
> f'(x)>0, f''(x)>0 , for x<h
> f'(x)>0, f''(x)<0, for x>h

1. Determine the value of a, b, c and d so that the curve y=ax^3+bx^2+cx+d will pass through the points (0,1) , (-3,7) and have a critical point at (-1,3)

The relationship of a capacitor voltage (volts) and time (seconds) is given by V = 95(1-e^0.1t ).

Plot the graph between t = 0 and t = 50 at 10 intervals.
Find the differentiation value at t = 10. Use calculus to verify your solution.

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

4, -8, and 2 + 5i

Find the Taylors expansion of f(x)=sin x at x=0.