Review Midterm Calculus

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Back

Front

The radius r of a circle is increasing at a rate of 5 ft per hour. Find the rate of change of the area (in square feet per hour) of the circle when the radius is 10 ft.

Back

Front

Back

Front

Back

Front

At which x-value is f continuous but not differentiable?

Back

The function is continuous but not differentiable at x = a.

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

State the product rule for differentiation.

Back

If f(x) and g(x) are functions, then the derivative of their product is given by: (f g)' = f' g + f g'.

Front

What is the chain rule in calculus?

Back

The chain rule states that if a function y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

Define the concept of continuity at a point.

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A function f is continuous at a point x = c if: 1) f(c) is defined, 2) lim (x -> c) f(x) exists, and 3) lim (x -> c) f(x) = f(c).

Front

What is the formula for the area of a circle?

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Tags

CCSS.7.G.B.4