We compute average velocity to estimate instantaneous velocity.

We find limits using numerical information.

In this section we use the graph of a function to find limits.

Compute limits using algebraic techniques.

Determine when a limit is infinite.

Find limits at infinity.

Find limits using the Squeeze Theorem.

In this section we learn the definition of continuity and we study the types of discontinuities.

In this section we learn a theoretically important existence theorem called the Intermediate Value Theorem and we investigate some applications.

In this section we learn the definition of the derivative and we use it to solve the tangent line problem.

We determine differentiability at a point

We learn how to find the derivative of a power function.

The following rules allow us the find the derivative of multiples, sums and differences of functions whose derivatives are already known.

In this section we compute derivatives involving $e^x$ and $\ln (x)$.

In this section we compute derivatives involving $\sin x$ and $\cos x$.

We compute the derivative of a product.

We compute the derivative of a quotient.

We compute the derivative of a composition.

In this section we compute derivatives involving $a^x$ and $\log _a(x)$.

In this section we compute derivatives involving $\tan ^{-1}(x), \sin ^{-1}(x)$ and $\cos ^{-1}(x)$.

We learn the derivatives of many familiar functions.

Use the differentiation rules to compute derivatives

We use the logarithm to compute the derivative of a function.

In this lesson we will use the tangent line to approximate the value of a function near the point of tangency.

In this section we analyze the motion of a particle moving in a straight line. Our analysis includes the position, velocity and acceleration of the particle.

In this section we interpret the derivative as an instantaneous rate of change.

We learn to compute the derivative of an implicit function.

In this section we discover the relationship between the rates of change of two or more related quantities.

In this section we learn to find the critical numbers of a function.

In this section we learn the Extreme Value Theorem and we find the extremes of a function.

We apply the Mean Value Theorem.

In this section, we use the derivative to determine intervals on which a given function is increasing or decreasing. We will also determine the local extremes of the function.

In this section we learn about the two types of curvature and determine the curvature of a function.

In this section we compute limits using L’Hopital’s Rule which requires our knowledge of derivatives.

We find extremes of functions which model real world situations.

In this section we learn to compute general anti-derivatives, also known as indefinite integrals.

In this section we examine several properties of the indefinite integral.

In this section we learn to reverse the chain rule by making a substitution.

We compute Riemann Sums to approximate the area under a curve.

In this section we learn to compute the value of a definite integral using the fundamental theorem of calculus.

In this section we learn to compute the value of a definite integral using the fundamental theorem of calculus.

In this section we use properties of definite integrals to compute and interpret them.

In this section we use definite integrals to study rectilinear motion and compute average value.

In this section we learn the second part of the fundamental theorem and we use it to compute the derivative of an area function.

In this section we prepare for the final exam.