40 Calculus Tutorials

These Calculus tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Calculus help you need, whether through these tutorials or through private tutoring lessons.

Limits

Limits are the underlying base to Calculus. We do not usually look at them as we work, but they are in virtually everything we do. They are a strange idea for math as well, because they are based on our perception rather than some calculation we do. To take a limit of a function, we…

intro to chain rule

The chain rule in calculus is finding the derivative for two or more products of themselves. For example F(x)= (x+3)^4 where F(x)= G(H(x)) and G(x)= (x)^4, H(x)= x+3. Then you would use the chain rule to find the derivative. This rule is simple, yet it can be hard to differentiate the different individual functions. So…

continuation of chain rule

The chain rule in calculus is finding the derivative for two or more products of themselves. For example F(x)= (x+3)^4 where F(x)= G(H(x)) and G(x)= (x)^4, H(x)= x+3. Then you would use the chain rule to find the derivative. This rule is simple, yet it can be hard to differentiate the different individual functions. So…

Continuity

This is a question with 2 equations, it will help show if an equation is continous or not based on if all the values in the equation give us a real answer or not and how to find what kind of continuity without a graph

The mean value theorem

the mean value theorem (MVT) is an extremely important theorem in calculus. it states that: If f is continuous on the compact a≤x≤b and differentiable on a< x

Implicit Differentiation Application: Sphere to Surface Area

Implicit differentiation is one of the most commonly used techniques in calculus, especially in word problems. It takes advantage of the chain rule that states: df/dx = df/dy * dy/dx Or the fact that the derivative of one side is the derivative of the other. Simple example: derivative of x + y = 3 is:…

Trigonometric Integrals

Still in integration where our objective is to find the anti derivative of a certain function, in this case trigononetric functions. But first we will be dealing with simple trigonometric integrals.

Integration by Parts

The integration by parts formula S udv = uv – S vdu is derived from the product rule of differentiation d (uv) = vdu + udv. From the derivative form we will be making the function or equation back to its original function though it is in product form. I will be giving example(s) how…

Why is the Integral an Anti-derivative?

We will use the following definitions: Anti-Derivative : The anti-derivative of a function f is a function F such that F' = f. Integral (area definition) : The integral of \int_a^b f(x) dx of f is the area under the curve f(x) from x=a to x=b. Let us define the area under the curve f

Logarithmic Differentiation

You need to use Logarithmic Differentiation when you want to find the derivative of a function that is in the (x^x) form. You start out by equating y to any function that is (x^x). You then apply logarithmic rules to the function by encasing “y” with ln and bringing the power of “x” down in…

^