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At the x-intercepts of the graph, the line crosses the x-axis. This means that the y-value at these points equals 0. We must therefore make x^2+2x equal to 0 and simplify the equation. x^2+2x = 0 is the s...

A production possibility frontier, or PPF, is a line showing the maximum level of output in an economy of one good or group of goods in terms of another. At any point on this line, the economy is operatin...

y=e^(x)*sin(x)   

Use the product rule:   y'=uv'+vu'    y=u*v          

Differentiate: u=e^(x)   u'=e^(x)    v=sin(x)  v'=cos(x)

Sub into the product rule: y'=e^(x)*cos(x)+e^(x)*sin(x...

In German, there are 3 ways of forming the past tense. The easiest 2 are the Perfect and Imperfect, and there is another slightly more complex form calle...

The structure of Sonata Form - consisting of an Exposition, Development, and Recapitulation (sometimes with Coda) - gives ample room for the execution of a musical argument. In the exposition, all musical...