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How to Use the Limit Laws in Calculus

If you know the limit laws in calculus, you'll be able to find limits of all the crazy functions that your pre-calculus teacher can throw your way. Thanks to limit laws, for instance, you can find the limit of combined functions (addition, subtraction, multiplication, and division of functions, as well as raising them to powers). All you have to be able to do is find the limit of each individual function separately.

If you know the limits of two functions, you know the limits of them added, subtracted, multiplied, divided, or raised to a power. If the

image0.png

you can use the limit operations in the following ways.

  • Addition law:

    image1.png
  • Subtraction law:

    image2.png
  • Multiplication law:

    image3.png
  • Division law:

    image4.png
  • Power law:

    image5.png

The following example makes use of the subtraction, division, and power laws:

image6.png

you find

image7.png

with the following calculations:

image8.png

Finding the limit using limit laws really is that easy!

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