Why indeterminate forms

We now encourage the reader to investigate each one of the terms shown in Table 5. An undefined expression involving some operation between two quantities is called a determinate form if it evaluates to a single number value or infinity. An undefined expression involving some operation between two quantities is called an indeterminate form if it does not evaluate to a single number value or infinity.

We will inspect multiplication more closely. This is like two ends of a rope being tugged and we do not know which side is going to win. We leave the remaining terms up to the reader to investigate and simply present the determinate and indeterminate forms of the expressions from Table 5. We are now in a position to introduce one more technique for trying to evaluate a limit.

This theorem is somewhat difficult to prove, in part because it incorporates so many different possibilities, so we will not prove it here. If the functions have similar growth rates, then then the limit approaches a constant. We now exemplify this idea of growth rate. Active 2 years, 11 months ago. Viewed 10k times. Paolo 1 1 gold badge 5 5 silver badges 22 22 bronze badges. DevX DevX 1 1 gold badge 3 3 silver badges 9 9 bronze badges.

Add a comment. Active Oldest Votes. There are helpful criteria, for instance asymptotic comparison, but no general theorem is possible.

Marc van Leeuwen Marc van Leeuwen k 6 6 gold badges silver badges bronze badges. Geoffrey Geoffrey 2, 12 12 silver badges 27 27 bronze badges. Aakash Kumar Aakash Kumar 3, 2 2 gold badges 11 11 silver badges 25 25 bronze badges. In the case you exhibited, we say the result is undefined. Cerbero Cerbero 1. Sign up or log in Sign up using Google. Sign up using Facebook.

Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. It is worth mentioning that some textbooks may refer to these techniques as factorization fraction reduction , rationalization, and Trigonometric rules, as does Khan Academy.

Together we will walk through countless examples, step-by-step, in order to see the power of factoring, common denominators, conjugate math, and some pretty awesome trigonometric rules as they help us find the solutions we desire. In fact, I consider this video lesson one of the most critical lessons in our limits chapter because the skills and techniques we learn in this video will enable us to find derivatives and integrals later in our calculus course.

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