Q1:

Use g(x) = (Ax + B)!/ where A and B are positive constants to answer the questions below. Use upper case letters for A and B. (a) Find g ' (x) = (b) Determine g ' (0) = (c) Find an equation for the tangent line to g at x = 0. Use y as the dependent variable.per square foot. A bottom will not be needed. A gardener is building a shed to protect his plants from hot weather. Its shape is the surface of a half cylinder with radius r and length h as shown. The material needed for the two flat semi-circular ends costs 10 dollars per square foot. The material needed for the upper curved portion costs 4 dollars Recall: The lateral (sides) surface area of a cylinder is given by A = 2xrh and the volume of a cylinder is given by V = azh Find the total cost, C(r) , for building this shed as a function of the radius if the volume inside must be 200 cubic feet. o C(r) = 10x/2 + 200 C(r) - 10*/2 + 1600 c(r) = 5x/2 + 800 C(r) = 20x/2 + 1600 o c(r) = x2 + 200 C(r) = x/2 + 1600Consider the graph of the following function. A Select the graph that could be an antiderivative of the graph shown above.(a) Consider lim ex X-+0 In(x) What does the numerator approach as x - co ? What does the denominator approach as x - ? Does L'Hopital's Rule apply? -Select- # What is the exact value of the limit? (b) Consider lim cos(ax) - cos(bx) where a and b are positive constants with a $ b . X- 0 x2 What does the numerator approach as x - 0? What does the denominator approach as x - 0? Does L'Hopital's Rule apply? ---Select- # What is the exact value of the limit