What am I doing when I take the derivative of a function?

The idea of the derivative is explained using the function x^2.

Need help finding solutions to HW

1. The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 320 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decreas ...continues

What am I doing when I integrate a function? (with no numbers at the top and bottom of the integration symbol)

Integration is explained using the example Sx^2dx.

Please explain the formal epsilon-delta definition of the limit.

The formal definition of the limit is explained using the example lim x->5 2x = 10.

Show me how to use the definition of the derivative.

The process of working with the definition of the derivative is shown using the example f(x)=3x-6.

Show me how to use the definition of the derivative.

The process for working with the definition of the derivative is shown using the example f(x)=x^2+5x-3.

Increasing functions: Comparing Functions

Explain why the graph of f(x) is rising over an interval a < or equal to x < or equal to b if f '(x) > 0 throughout the interval. What can you say about the graph of f if f '(x) is less than zero on a < or equal to x < or equal to b?

U substitution

U substitution is explained using the example S4x(x^2+1)^5dx without and with limits of integration.

Integrate sin^2(x)?

The steps for integrating sin^2(x) are shown with explanations of each step.

Tabular integration

I am integrating x to a power times sin, cos or e to a power using repeated integration by parts, but it is very cumbersome. Is there a better way?