Review Midterm Calculus

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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

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Front

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Front

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

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

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What is the definition of a derivative?

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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.

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State the product rule for differentiation.

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

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What is the chain rule in calculus?

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

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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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