Calculus Answers

Find (f + g)(x).

f(x)=square root 3x+7 , g(x)=square root 3x-7

Determine the volume of the solid bound between the sphere x^2+y^2+z^2=R^2 and the cylinder x^2 +y^2=r^2, where R>r (such shapes are called spherical rings or napkin rings).

What is the common property between determinants, integrals and derivatives?

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.

Expand (4-x) / (2-x)(1-x)^2 in ascending powers of x, stating when the expansion is valid; also write down the coefficient of x^n.

Find f(x)=x 3n

Find f(x)=(7x 4 −5x 3 )

Find f(x)=x 27

Differentiate with respect to
x: f(x)=(ax 3 +bx)

Sketch the region bounded by f(x) = 1+2ex, g(x) = 1+4e−x, x = −1 and x = 1. Using calculus, find the area of the region, showing all the working. Express your answer in simplified exact form.

step by step working out