Evaluation and calculation of delta z and a total differential.

(a) evaluate f(1,2) and f(1.05,2.1) and calculate delta z. (b) use total differential dz to approximate delta z using equation f(x,y) = xe^y

Maximum value and directional derivative

Find the gradient of the function and the maximum value of the directional derivative at the indicated point: g(x,y)= arccos xy pt. (1,0) v=i+5j

Exponential Equations : Word Problem

The population of the green deer in 1999 was 17000. In 2003 there were only 15000. Write an exponential equation to express the poulation decrease p(t) in terms of t years.

Derivative of a Function: Quotient Rule

Using the quotient rule, find the derivative of f(x)= 3-2x-x^2/x^2-1

Derivative of a Function: Product Rule

Use the product rule find derivative of h(t)= cubed root of t * (t^2+4)

Function as a Composition: Domain Calculations

What are the formulas for f+g, f-g, fg, and f/g, and the domains of the functions if f(x)= 3x-2, g(x)= |x|

Quick Calculation of Laplace Integral

Please see the attached file for the fully formatted problem. Construct the quickest method to calculate the Laplace Integral. I = S e^(-x^2) dx infinity --> infinity

10 Calculus Problems

Please see the attached file for the fully formatted problems. Problems involve: parametric equation of line segment, volume of a parallelipiped, sketching a plane gven the equation, finding rectangular equations, center and radius of a sphere using the equation of a sphere, force vector problems.

Maximum of a function in a closed interval.

Find the maximum of the following function f(x)=x(1-x) over [0,1]

Derivative

Find f'(0) where f(x)=(x+1)(x+2)...(x+1000)