Finding the number of units to be sold to maximize the profit

problem is attached

Finding Derivatives

problem is attached

Integration of a definite integral

True or false: the final result of an integration of a definite integral is a number

Dy/dx

please see attached

Derivitive of the function

please see attached

Find open intervals

problem is attached (please do not put solution in excel --I don't have it)

Integration

If f(x) = int_{1}^{x^{2}} t^2dt then f'(x)= then f'(5)=

Taylor Polynomials

f(x) = ln5 + ln(1-1/5x) Using substitution in one of the standard Taylor series, find the Taylor series about f for 0. Give all terms up to the term in x^3.

Equation of the tangent line

Find the equation of the line to y = x^(sin x) at the point [(pie/2),(pie/2)] Show all work and reduce to lowest terms.

Integrate the differential equation

(x^2 + 3y^2) dx - 2xydy = 0 Integrate the differential equation. Complete step by step work must be shown and reduced into lowest terms.