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 √16 + h − 4 / h

Accepted Answer

Welcome back. Every once in another video, calculate the following limit or specify that it does not exist limit. When V approaches zero of square root of 36 plus V minus six divided by V were given for answer choices. A +16 B 1/12 C 1/18 and D, the limit does not exist. So basically, first of all, we can begin solving this limit by direct substitution or given our limit 36 plus V square root of that minus six divided by B if we apply the direct substitution, the approach is zero. So we get square root of 36 minus six divided by zero. And this gives us zero divided by zero, which is an indeterminate form, meaning we want to eliminate that indeterminate form. And in this case, what we can do is basically multiply both sides of the fraction by the conjugate of the numerator. Our conjugate is going to be square root of 36 plus V plus six. So basically the opposite sign instead of taking the difference, we're going to get the addition of the two terms. So we're taking the sum between 36 plus P square root of that plus six as our conjugate. And we have to multiply the denominator by the same term. So squared of 36 plus V plus six. Now, for the numerator, let's apply the formula for the factorization of the difference of squares in a reverse, we get limit when V approaches zero of the first term squared. So we get 36 plus V minus the square of the second term. So six squared gives us 36 in the denominator, nothing changes. We have V multiplied by square root of 36 plus V plus six. Now let's simplify the numerator, 36 minus 36 gives a zero. And then we end up with B divided by V those cancel each other out. So our numerator only has one remaining. And in the denominator, we have 36 plus V square root of that plus six. And now we can apply direct substitution once again to see if we get a finite number. So the numerator has one. In the denominator, we end up with 36 plus zero. That's 36. And we're taking square root of 36 plus six. Now, square root of 36 is six. So we end up with one divided by 12, 6 plus six is 12, right? And this is a finite number, meaning we have successfully evaluated the limit and this corresponds to the answer to B. 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 √16 + h − 4 / h

Key Concepts

Limits

Rationalizing the Numerator

Indeterminate Forms

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