Calculus 1st Semester Review

Front

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

Back

The limit of a function describes the value that the function approaches as the input approaches a certain value.

Front

True/False: If the limit of a function exists at x=c, then f(c) exists.

Back

False. A function can have a limit at a point without being defined at that point.

Front

Find the derivative of y = 2x^-1.

Back

y' = -2x^-2.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

What is the power rule for differentiation?

Back

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

Front

Find the limit: lim (x -> 2) (4x^2 - 3).

Back

The limit is 8.

Front

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

Back

A function is continuous at a point if the limit exists at that point and equals the function's value at that point.

Front

What is the difference between a one-sided limit and a two-sided limit?

Back

A one-sided limit considers the value of the function as it approaches from one side (left or right), while a two-sided limit considers both sides.

Front

Find the derivative of y = 3x^3 + 2x^2 - x + 5.

Back

y' = 9x^2 + 4x - 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.