AB Sem 1 Final Review

Front

What is the formula for the tangent line approximation of a function f at a point x=a?

Back

The tangent line approximation is given by: f(a) + f'(a)(x - a).

Front

What does it mean for a function to be differentiable at a point?

Back

A function is differentiable at a point if it has a defined derivative at that point, meaning the function has a tangent line at that point.

Front

How do you find the rate of change of the area of a circle with respect to its radius?

Back

The area A of a circle is given by A = πr². The rate of change of area with respect to time is dA/dt = 2πr(dr/dt), where dr/dt is the rate of change of the radius.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

What is the limit of a function as x approaches a certain value?

Back

The limit of a function as x approaches a value is the value that the function approaches as x gets arbitrarily close to that value.

Front

What is the definition of the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.71828.

Front

What is the derivative of e^x?

Back

The derivative of e^x with respect to x is e^x.

Front

What is the relationship between the derivative and the slope of a tangent line?

Back

The derivative of a function at a point gives the slope of the tangent line to the graph of the function at that point.

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by C = 2πr, where r is the radius.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if you have a composite function f(g(x)), then the derivative is f'(g(x)) * g'(x).