Calculus Answers

Evaluate the limits

"Lim"

Xto + sum to infinity

5xcube-2xsquared +1 divide by 1-3x

X³-2x is it odd function or even

Differentiate the following functions:

y = (t^3 - 5)^1/a

1. Differentiate the following functions:

(a) y = x^3 cos

(b) y = e^x/sin 2x

Differentiate the following functions:

(a) y = `4√x + 4/x + 3 ln x

5a) A projectile is fired vertically upwards with height h given by: h = 25t - 4.9t^2 where 0 ≤ t ≤ 5

Find expressions for the velocity and acceleration. Determine the maximum

height reached by the projectile.

5. A projectile is fired vertically upwards with height h given by: h = 25t - 4.9^2 where 0 ≤ t ≤ 5

4. An electrical voltage E is given by: E = ( 8 sin50πt + 14 cos50 πt ) volts. Where t is the time in seconds. Determine the maximum value of the voltage

3. Copper is supplied to a company in rectangular sheets measuring 108 by 45 cm. The company wants to make open boxes in the shape of cuboids, with the maximum volume possible and the minimum of waste. If the height of the box is x use differentiation to find the dimensions and hence the maximum volume

2. Find the gradient of the curve y =4 sin 2x + 3cos 1/2x, at x = TT/3