Cumulative Calculus Review Sep Oct Nov

Front

What is the limit as x approaches 4 of (x^2 - 16)/(x - 4)?

Back

8

Front

What do we find when we take the derivative of a function?

Back

The slope of the tangent line.

Front

What is the derivative of the constant function f(x) = 7?

Back

0

Front

Solve the equation log_2(x + 5) = 3.

Back

3

Front

If h(x) = f(x) - g(x), how do you find h'(1) using the derivatives of f and g?

Back

Use the rule h'(x) = f'(x) - g'(x) and evaluate at x=1.

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).