Calculus Answers

Integrate the following with respect to x :

(a) (5x-3)^4

a) The equation of motion of a particle is ,where s=t^3-3t is in metres and t is in seconds. Find i) the velocity and acceleration as functions of t, ii) the acceleration after 2 seconds, iii) the acceleration, when the velocity is 0.

A friend asked you for some help in designing a poster. The poster your friend is designing must contain 50 square inches of printing with margins of 4 inches at the top and bottom, and 2 inch margins on each side. Your friend wants to use the least amount of paper possible. What overall dimensions (length and width) should you tell your friend to design the poster with in order to make this possible?
Draw a sketch of the situation and label all given quantities.

Find f(0,0) and fr(x, y), where (x, y) = (0,0) for the following function
if x, y is equal to x y cube upon x square + y square if x, y does not is equal to 0, 0 and 0, x, y is equal 200

Integrate the following function w.r.t. x using substitution : 1) x^3√x^4+1 dx . lim 0 to 1. 2) tan^7x sec^2x dx lim 0 to π/4 . 3) sec^2(cosx) sinx dx

that means of the functions f /g where f x, y is equal to 2 x y and g x, y is equal to x square + y square is r square which statement is true or false give reason

a) Express the following surfaces in spherical coordinates
i) xz=3
ii) x2 + y2 - z2=1
b) Find the cylindrical coordinates of the points where the Cartesian coordinates are
i). (6,6,8)
ii) (√2,1,1)

The domain of the function flg where f(x, y) = 2xy and g(x, y) = x² + y²is R.

Find the area bounded by y=√x and y=x^3+2 and x=4 and Y-axis
Make a sketch, use vertical elements, show the element of area with its dimensions and corresponding differential of area.