Business Calculus

Q1

Find dy. Y= X 11 - dy = (Simplify your answer.)570 Find dy for the function y = X dy = (Simplify your answer.)Find the indicated quantities for y = f(x) = 5x f(3 + Ax) -f(3) (A) Simplify AX (B) What does the quantity in part (A) approach as Ax approaches 0? f(3 + Ax) - f(3) (A) = AXFind dy for y = (9x + 1)2. dy = (Simplify your answer. )Fer 3r = fix1=x4 6x+2, nd y and sly, given x=l and x=.3. E) :13; = D Hype an integer er a decimal.) Evaluate dy and Ay for the function below at the indicated values. 5 y = f(x) = 64 1 -- * x = 4, dx = Ax = - 0.2 X dy =A cube with sides 8 inches long is covered with a coat of fiberglass 0.6 inch thick. Use differentials to estimate the volume of the fiberglass shell. The volume of the fiberglass shell is approximately |] in.Let x] = 5x2 + 211:: + s. {A} Find y and dy for the function f at x = 0.5. {B} Graph the functions y and d'f from part A. {(3} Compute the values of y and d1; from part for x= ISLE. E) {A} Find y and ti}; for the function f at x = l].5. y=|:| [Use the symbol in the math palette as needed. Do not factor.) Find dy. 4 3 y = x (2 -4x). dy =_ 380 1 For a company that manufactures tennis rackets, the average cost per racket is found to be C = T + 4 + 3x for x 2 1, where x is the number of rackets produced per hour. Use the differential to approximate the change in average cost per racket ifproduction is (A) increased from 25 per hour to 32 per hour and (El) increased from 35 per hour to 42 per hour. E) (A) If production is increased from 25 per hour to 32 per hour the average cost per racket will E] by approximately $:| per racket. An egg of a particular bird is very nearly spherical. The radius to the inside of the shell is 7 millimeters and the radius to the outside of the shell is 7.2 millimeters. 4 Use differentials to approximate the volume of the shell. [Remember that V(r) = ,xr , where r is the radius.] The volume of the shell is approximately mm (Round to the nearest hundredth.)The shape of a colony of bacteria on a Petn' dish is circular. Find the approximate increase in its area if its radius increases from 30 mm to 36 mm. [Recall that the area of a circle is A = \"2] The estimated change in area is I: mm2_ (Round to Mo decimal places as needed.)