Calculus Answers

A small startup company produces lens and apertures for DSLR camera that they sell through a website. After extensive research, the company has developed a revenue function as follows

R(x,y) = x(110-4.5x) + y(155-2y)

in thousand ringgit where x is the number of lens produced and sold in thousands and y is the number of aperture produced and sold in thousands. The corresponding cost function is

C (x,y) = 3x2 + 3y2 + 5xy – 5y + 50

in thousand ringgit. If you are the investors, find the production levels that maximize the revenue. Then, would you invest or not in the company? Justify

The bulk density of the chips was measured by weighing a batch of 195 liters of chips. The measurement result is 42.5kg. The volume was measured to within ± 2.5 liters. At what accuracy should the mass be measured to determine the bulk density to an accuracy of at least ± 3%?

The ball circumference was measured and the result was p = 38.77 ± 0.20cm. By what accuracy can the ball surface be calculated?

3. Let L be the length of the curve x=e^y from (1,0) to (e,1), integrating with respect to x an integral expression for L is_____.

4. Let be the length of the curve y=ln(x) from (1,0) to (e,1), integrating with respect to y, an integral expression for L is_____.

3. Let L be the length of the curve x= e^y from ( 1,0) to (e,1), integrating with respect to x, an integral expression for L is____________.

4. Let L be the length of the curve y= ln(x) from (1,0) to (e,1), integrating with respect to y, an integral expression for L is _________.

1. Let L be the length of the curve y= x^5 + 8/ 16x^2 from x=2 to x=3, an integral expression for L is ________.

2. Let L be the length of the curve x= y^4/8 + 1/ 4y^2 from y= 1 to y=4, an integral expression for L is______.

1. Find the area of the regionenclosed by the curves x=y^2-2 and x=y.

Find the area of the region enclosed by the curves x= y^2-2 and x=y.

1. Find the area bounded by the curve y= x^2+x+4, the x axis from x=1 to x=3.

1. Find the area bounded by the curves y= x^2-4, y=0 and x=4.