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"Show that the indicated function is a solution of the given differential equation; that is, substitute the indicated function for y to see that it produces an equality"
-x(dy/dx) + y = 0; y = Cx
Apply DeMoivre's Theorem to solve the following: any angles that are multiples of pi/6, pi/4, pi/3, pi/2 or pi must be converted back into regular complex form!
Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).
Use a triple integral and an appropriate change of coordinates to calculate the volume of the region bounded by the xy -plane, the surface z = x^2 + y^2 and the cylinder over x^2/9 + y^2/4 = 1 .
Fibonacci proved that if the sum of two consecutive integers is a square (that is, if n + (n - 1) = u^2 for some u), then the square of the larger integer will equal the sum of two nonzero squares
State Euler's Circuit Theorem. Explain why this theorem should be true and explain Cantor's Diagonalization Argument. Give examples and explain what this argument was used for.
A box with a square base has length plus girth of 106 in. (Girth is the distance "around" the box.) What are the two possible lengths of the box, if its volume is 2200 in3?
Allison is saving money to buy a video game system. In the first week, her savings were $8 less than 2/5 the price of the system. In the second week, she saved 50 cents more than 1/2 the price of the system.
Use partial decomposition to integrate. (2x^2-x-20)/(x^2+x-6 ). (sint)(4cos^2t-1)/(cost)(1+2cos^2t+cos^4t)
Calculate and interpret the coefficient of determination
Use implicit differentiation to find an equation of the line tangent to the curve x^2 + y^2 at the point (3,-1). Use implicit differentiation to find an equation of the line tangent to xy=12 at the point (4,3)
The speed of a passenger train is 10mph faster than the speed of a freight train. The passenger train travel 310 miles in the same time it takes the freight train to travel 260 miles. Find the speed of each train.
An open box is to be made from a square piece of sheet metal, 20 inches on a side, by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.
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