Review Midterm Calculus

Front

What is the derivative of the function f(x) = (6x^2 - 5x)^7?

Back

f'(x) = 7(6x^2 - 5x)^6(12x - 5)

Front

What does the derivative of a function represent?

Back

The derivative represents the rate of change of the function with respect to its variable, indicating the slope of the tangent line at any point on the graph.

Front

What is the limit of a function?

Back

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

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow2}rac{x^2-3x+2}{x^2-4}@@

Back

Front

What is the relationship between speed and acceleration?

Back

Speed is the magnitude of velocity, while acceleration is the rate of change of velocity with respect to time.

Front

How do you find the speed of an object from its position function s(t)?

Back

To find the speed, first find the derivative of the position function s(t) to get the velocity function v(t), then evaluate v(t) at the desired time.

Front

What is the Fundamental Theorem of Calculus?

Back

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1).

Front

What is the chain rule in calculus?

Back

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that the limit does not approach a finite value.