Math (Calculus) Assignment essay writing services

Please show all the work. Thank you. I will upload the file with the problems, and I will copy them in here as well.

HOMEWORK ASSIGNMENT #7
Due by 2:55pm on Wednesday, March 18.

All of the problems have equal weight. Always show your work or explain how you got your answer. Don’t assume it is obvious.

1) Find the infinite Taylor series expansion of the function y = xe^x about x = 0.

2) a) Let f(x) = ln(x + 1), where x > –1. Write down Taylor’s formula with remainder for the function f(x) around x0 = 0, where the remainder entails the 2nd derivative.
b) Using linear approximation, give an estimate of ln(1.02).
c) Using the remainder, compute the maximum possible (absolute) value of the error in the above estimate.

3) Using the definitions of convexity and concavity (i.e., without the use of derivatives) show that the function y = a + bx, where a and b are constants, is both convex and concave.

4) Let f and g be two strictly concave functions and let function h be defined by
h = af + bg, where a > 0 and b > 0 are constants. Using the definition of strict concavity (i.e., again without the use of derivatives) show that h is strictly concave.

5) Consider a profit maximizing monopoly. The demand for the monopoly’s product is given by Q = ln(a – bP) and its cost function is C(Q) = ce^Q, where the parameters a, b, c are all positive. Let Q* be the monopoly’s optimal (profit-maximizing) output. Derive an expression for ∂Q*/∂a and determine its sign.

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