Determine if the following piecewise defined function is differentiable at x = 0. 1/1 f (x) = 2/1 x 4 x -4 x greater than or = 0 x2 +2 x -4, x less than 0. What is the right-hand derivative of the given function?

Find the sum of the first 8 terms of the following sequence. round to the nearest hundredth if necessary.

(! ) three cylinders have a height of 8 cm. cylinder 1 has a radius of 1 cm. cylinder 2 has a radius of 2 cm. cylinder 3 has a radius of 3 cm. find the volume of each cylinder

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.