Building Blocks of Calculus

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Calculus is not just a bunch of confusing topics! Learning about the inner connections of calculus can make the topic less difficult!


Limits create the support system for calculus. Limits are the reason why differentiation and integration actually work!


Differentiation finds the slope at a point by moving the slopes of the secant lines infinitely close together (limit process) to produce the slope of a single tangent line.

This process of finding the slope at a point allows us to find the instantaneous rate of change for a moving vehicle, the extrema of an equation to help businesses make maximum profit, and the rate at which something is increasing or decreasing in respect to time.


Integration finds the area under a curve by slicing the area into an infinite amount of rectangles and adding them up. Where do limits play a role? Well, integration undoes differentiation and the derivative is used to find the integral! In addition to running the widths of the rectangles to zero as you keep adding more.

This process of finding the area under a curve allows us to find the volume of a solid that may not be a normal geometric shape, and the area of a cross section of an abnormal geometric shape. This is specifically helpful for engineers.

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