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Calculus and Analysis

Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the iterated integral :  ^1_0  ^(x^2)_0 xy dy dx : is the integral symbol

Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the iterated integral:  ^2_0  ^2x_0 (1 + y) dy dx : is the integral symbol

Solution of Differential Equation

Verify that y_p , where y_p(x) = sin 2x, is a solution of the differential equation: y'' - y = -5 sin 2x. Use this fact to find the general solution of the equation

Differential Equation Solution Function

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. Find the general solution of the differential equation: y''' + 2y'' + y' + 2y = 0

Differential Equation : Basis

Verify that the given functions form a basis for the space of solutions of the given differential equation: x^2 y'' - 2xy' + 2y = 0, f_1(x) = x, f_2(x) = x^2, x > 0

General calculus

20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain

Differential Equation

Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process. 1. The drug Valium has a half-life in the blood of 36 hours. Assume that a 50-milligram dose of Valium is taken at time t=0. Let m(t) be the amount of drug in the blood in milligrams t hours

Solve: Multivariate Calculus

Please see the attached file for full problem description. (a) where R is the region in the first quadrant which lies inside the circle x^2 + y^2 = 2x and outside the circle x^2 + y^2 = 1. (b) If f(x,y) = x/y and h(x,y) = (1/2)x^2 - 4y find the rate of change of f(x,y) at the point (2, -1) in the direction in which h(x,y)

Parametric Equation Position and Range

Professional golfer Nancy Lopez hits a golf ball with a force to produce an intinial velocity of 175 feet per second at an angle of 35 degrees above the horizontial. She estimates the distance to the hole to be 225 yards. A) Write the position of the ball as a pair of parametric equations. (I know that it is x=175tcos(35)and

Vector Problem: Force up Ramp

What would be the force required to push a 100-pound object along a ramp that is inclined 10 degrees with the horizontal?

LAPLACE TRANSFORMS

Please see attachment. Require problems solving, also explanations etc for better understanding.

Working with Maximum Resulting Error in Calculation of Area

Show all work. Please DON'T submit answers back to me as an attachment. The dimensions of a closed rectangular box are found by measurement to be 10 cm by 15 cm by 20 cm, but there is a possible error of 0.1 cm in each. Use differentials to estimate the maximum resulting error in computing the total surface area of the box.

Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. Determine whether the function is homogenous. If it is, state the degree: f(x, y)=5x^2 + 2xy

Calculus differential equation

Find the order of the differential equation and determine whether it is linear or nonlinear: y^(4) + 3(cos x)y''' + y'=0