Find the following limits or state that they do not exist. Ass...

Question

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 (5 + h)^2 − 25 / h

Accepted Answer

Welcome back, everyone calculate the following limit or state that it does not exist limit. When K approaches zero of four plus K squared minus 16 divided by K, there are four answer choices ass eight B 12 C 16. Indeed, the limit does not exist. So first of all, let's apply direct substitution limit. When K approaches zero of four plus K squared minus 16 divided by K. When we apply direct substitution, we get four squared minus 16 divided by zero. And that's zero divided by zero, which is an indeterminate form because this is an indeterminate form. We want to eliminate that. And we can do that by applying the factorization. We're going to look at the numerator and we're going to notice that this is a difference of squares 16. It is essentially four squared, right? So now let's apply the factorization formula. It says that whenever we have A squared minus B squared, this difference can be factored out as A minus B multiplied by A plus B. And our A is four plus K, our B is four. So we get four plus K plus four multiplied by four plus K minus four in the denominator nothing changes. We have K and this simplifies to limit one K approaches zero of K or minus four gives us zero. We end up with K in parentheses, we have K plus eight divided by K and now we can eliminate that hole. We have K as the common factor. So we are evaluating the limit. When K approaches zero of K plus eight, we can apply the direct substitution once again and we get zero plus eight, which is simply eight. This is a finite number, meaning we have evaluated the limit and this is the answer to a eight. Thank you for watching.

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.
lim h→0 (5 + h)^2 − 25 / h

Key Concepts

Limits

Derivative

Algebraic Simplification

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