Calculus Answers

Determine wether the following functions is continuous on the given interval. f(x) = √4-x²

if the base X of the right triangle shown is increasing at the rate of 3 inches per second and the height Y is decreasing at the rate of 2 inches per second, find the rate of change of the area of the triangle when X = 5 inches and Y = 7 inches. Label the units on your answer

expand (1+x)^-2 using binomial theorem

Find y' if x^{y^2} = y^{x^2}

Determine the volume of the solid generated when the region bounded by the curve y^2=x^3 and the x-axis, is revolved about the line y=2

a. for the top and bottom of the box costs P30 per square centimeter and the material for the sides cost P15 per square centimeter. Find the dimensions of the box so that the total cost of material is the least possible and all its dimensions do not exceed 20cm.

by using squeeze theorem shaw that the lim of 1-coax/x² =0 as x tends to 0

u( x, y) = e^x(xsiny+ycosy) find the differentials