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Problem 59 Medium Difficulty

If $ \displaystyle \lim_{x \to 1}\frac{f(x) - 8}{x - 1} = 10 $, find $ \displaystyle \lim_{x \to 1}f(x) $.

Answer

8

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Video Transcript

in this problem. Number fifty nine of this tour Calculus Ace Edition, section two point three If the limit is experts, is wonder of the function half of X, minus eight over X minus one is he quoted ten find The limit is expert is one of the function. So since we're given this definitive statement that this woman is equal to ten all user limit laws to, ah rewrite this limit instead, as the Limited six pushes one of F minus the limited experts a sick one of eight Tiger Bhai and Element is ex purchase. One of the quantity x minus one crony calls attention. So we've used a limp laws that allow us to separate this quotient within the limit into a division of to limits and then the difference of limits in the top and the difference instead of a limit to the difference of limits at the top. And notice that this term here he said to me, one to solve for So let's go ahead and do that. I want to write about Science Limited Express on the ref minus Tell a man his ex precious one of eight. It's equal to ten times's limit his expressions wanted. Explain this one. We can you know the other element to the right hand side. So on the left and saying we have limited express is one of F equals ten times limit and exporters one that it quantity experience one a month element x x perches wanted Great. Now its exports has won This quantity explain. It's one is equal to one minus one or a zero and in time zero zero. So end of kidding is that the limit, as an expression of wonder, is equal to zero plus is limited. The limit is export. Just want to eat a being in a constant value. Therefore telling it is equal to eight. And this is our final answer as to what the limit is. Export is one of the office.