AP Calculus Midterm Review

Front

What is the limit?

Back

The limit is a fundamental concept in calculus that describes the value that a function approaches as the input approaches a certain point. In this case, the limit is 12.

Front

Find dy/dx by Implicit Differentiation: x^3 + y^3 = 36

Back

The derivative dy/dx is found using implicit differentiation, resulting in dy/dx = -x^2/y^2.

Front

What is the derivative of sec(x)?

Back

The derivative of sec(x) is sec(x)tan(x).

Front

If the radius r of a sphere is increasing at 0.3 inches per second, what is the rate of increase in volume V when the surface area S is 100π square inches?

Back

The rate of increase in volume V is 30π cubic inches per second.

Front

Differentiate f(x) = (2/x^5) - 5.

Back

The derivative f'(x) is -10x^(-6).

Front

Define the derivative.

Back

The derivative represents the rate of change of a function with respect to a variable. It is the slope of the tangent line to the graph of the function.

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

Front

State the product rule for differentiation.

Back

The product rule states that if u and v are functions of x, then the derivative of their product is given by (uv)' = u'v + uv'.

Front

What is the chain rule in calculus?

Back

The chain rule is a formula for computing the derivative of the composition of two or more functions. If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

Explain the concept of limits approaching infinity.

Back

Limits approaching infinity describe the behavior of a function as the input grows without bound. It can indicate horizontal asymptotes or unbounded growth.