Using the definition of the derivative to differentiate.

Use the definition of the derivative f(x) = x + sqrt(x) to prove D[x+sqrtx]=1+1/2sqrtx

Finding constants to satisfy a differential equation.

Find the constants A, B, and C such that the function y=Ax^2+Bx+C satisfies the differential equation y^n+y'-2y=x^2.

Using related rates to answer a pulley question.

Two carts A and B are connected by a rope 39 feet long that passes over pulley P. The point Q is on the floor directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 2 ft/sec. How fast is cart B moving toward Q at the instant cart A is 5 feet from Q? Express solution using related rate n ...continues

mu''(t) + ku(t) = 0

Suppose m and k are positive numbers. Find u so that mu''(t) + ku(t)= 0 for all numbers t and u(0)=1 and u'(0)=2. (note: u'' = second derivative of u)

Finding a Polynomial

Find a polynomial p so that: p''(t)+3p'(t) + 2p(t) = (t^2)-2 for all numbers t. (note: p''= p double prime and t^2 = t raised to the power of 2)

mu''(t) + ku(t) = 0

Suppose m and k are positive numbers. Find u so that mu''(t) + ku(t)= 0 for all numbers t and u(0)=1 and u'(0)=2. (note: u'' = second derivative of u) Please clarify any shorthand that you are using. Thanks!

Outline a Computer Code in C++ to Obtain the Numerical Approx to ODE. using Euler's method is the simplest numerical method for approximation solving initial value ODE'S.

Outline a computer code for obtaining numerical approximations to y on [0,1] so that y(0)= 0 and y'(t) = ((y(t))^2) + t^2 for all numbers.This is being solved by computer code in c++ to obtain numerical approx to ODE. Using Euler's method is the simplest numerical method for approximation solving initial value ODE'S.

Outline a Computer Code in C++ to Obtain Numerical Approx to ODE

Outline a computer code for obtaining numerical approximations to y on [0,1] so that y(0)= 0 and y'(t) = ((y(t))^2) + t^2 for all numbers t.

A word problem involving marginal density, conditional density and proportion.

A tobacco company produces blends of tobacco with each blend containing various proportions of Turkish, domestic and other tobacco. The proportion of Turkish and domestic in a blend are random variables (X = Turkish and Y = domestic) with joint density function f (x,y) = { 24xy, 0 < or= x < or=1, 0 < or = y < or=1 ...continues

Sketch direction fields for the following ODE's

Sketch the direction fields for the following ODE's. Make use of isoclines wherever possible. a. y' = y - x + 1 b. y' = 2x c. y' = y - 1 d. y' = xsquared + ysquared - 1 e. y' = y - xsquared Please note y'=y prime. It looks diff, when i see the ? #2. In each direction field above sketch integral curves for which ...continues