7) Write a Table that meets the following conditions a) limx...

Transcript

00:01 We are asked to find the limit as x approaches 1 of f of x to the two -thirds power, and we're also given that the limit as x approaches 1 of f of x equals 8.

00:11 So how do we go about tackling this question? well, the first law that we need to use is our power rule law.

00:19 The way that that works is, i'll write it out for you, the limit as x approaches a of f of x to some exponent n, this will equal the limit as x approaches a of f of x the whole thing to the nth power now there is one caveat is that n is a positive positive integer that's the first law that we're going to use the second law that we're going to use is the root law that one is very similar to the power law, not exactly the same, but very similar to it.

01:08 It's that if you have some ffx to the root n power, this will equal the whole thing to the root n power.

01:16 What i mean is limit as x approaches a of ffx, whole thing, the root n power.

01:24 And n here also has to be some positive integer.

01:31 Make sure both of these are highlighted in your notes.

01:36 Now, i want to point something out.

01:37 The reason why we can't just apply the power rule to this problem and solve it is because n is not a positive integer.

01:45 And it's certainly positive.

01:46 It's two -thirds.

01:48 But it is not an integer.

01:49 N is two -thirds.

01:50 It's not an actual whole number.

01:52 So how do we go about doing this? well, the first thing that we're going to do is we're going to split this apart.

01:58 We're going to split this first...

Question

7) Write a Table that meets the following conditions a) \lim_{x \to 3} f(x) = 8 b) \lim_{x \to 1^{-}} f(x) = 2^{+}

Question

7) Write a Table that meets the following conditions a) \lim_{x \to 3} f(x) = 8 b) \lim_{x \to 1^{-}} f(x) = 2^{+}

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