Calculus

a Write the volume V of a cube as a function of the side length s. b Find the instantaneous rate of change of the volume V with respect to a side s. c Evaluate the rate of change of V at s=1 and s=5. d If s is measured in inches and V is measured in cubic inches, what units would be appropriate for dV/ds? 2. a Write the area A of a circle as a function of...

Find the unit tangent vector Tt and the principal unit normal vector Nt to the curve at t=1

Evaluate the following limit: 9. Evaluate the following limit: limlimits _xto 0frac sin 25x4x limlimits _xto 5frac x-5 square root of x- square root of 5

Find the absolute maximum and minimum values of the function fx,y=2+2x+2y-x2-y2 on the triangular region in the first quadrant bounded by the lines x=0,y=0 , and y=9-x. maximum value =2 at 0,0 minimum value =-61 at the points 0,9 and 9,0 maximum value = 19/5 at 3/9 , 6/9 minimum value =-61 at the points 0,9 and 9,0 maxmum vatue = 7/2 at 1/2 , 1/2 minimum val...

Find dy/dx for each of the following: a x3-y3=4

Find the average rate of change of p with respect to t over the interval 1 to 5 days. b. Which of the following is a correct expression for the instantaneous rate of change at t=2 2 A. limlimits _hto 0frac p2+h-p2h B. limlimits _hto 0frac p2+h-p2-h2 C. limlimits _hto 0frac p2+h-ph2 D. limlimits _hto 0frac p2+h-p2-hh

Find dy/dx for the equation x3-3xy+y2=11 [1]-[2]+[3]+[4]=[5] dy/dx =[6]/[7] Place expression in order of # for derivative and dy/dx 1 : : -3x+2y 2 ⅱ -3y 3 -3x2+3y 4 0 5 : 2y dy/dx 6 ::-3x dy/dx 7 ::3x2

OSCalc1 4.4 1 Use the Mean Value Theorem and find all points 0

Find f'-3 if fx=frac x45-5x. f'-3=- 133/5 Simplify your answer. Type an integer or a fraction.

a S8, S dl 3 paints an 4 oll 5 Pointa: 0 of 1 Suppose that the total proft in hundreds of dollars from selling x items is given by Px=5x2-6x+10 2 Complete partis a through d Below a. Find the average rate of change of profft as x changes from 4 to 6. $ 4400 per item b. Find the average rate of change of groft as x changes from 4 to 5. $ 3000 par itam s. Fi...