(1) Use the graph of the function f to determine the...

(1) Use the graph of the function f to determine the following limits (a) $\lim_{x \to -5^{-}} f(x)$ (b) $\lim_{x \to 0^{+}} f(x)$ (c) $\lim_{x \to 2^{-}} f(x)$ (d) $\lim_{x \to 2^{+}} f(x)$

Transcript

00:01 Let's find the limits using the graph of f of x.

00:04 In part a, we determine the limit of f of x when x approaches negative 8 from the right.

00:11 So when we look at the graph, this is where x is approaching negative 8 coming from the right.

00:18 And when x approaches negative 8 from the right, f of x approaches negative 6.

00:24 This one is negative 6.

00:26 So the limit is negative 6.

00:27 And now in part b, we determine the limit of f of x when x approaches negative 2 from the left.

00:36 So we have to look at here.

00:38 This is where x is approaching negative 2 from the left.

00:43 And we see that f of x is approaching 3.

00:46 So this limit is 3.

00:49 Now let's do part c.

00:50 Here we find the limit of f of x when x approaches negative 8.

00:55 For this we should calculate both the left and right side limits we already calculate the right side limit of f of x when x approaches negative 8 that equals negative 6 now let's calculate the left side limit of f of x when x approaches negative 8 so this is where x is approaching negative 8 coming from the left and clearly we see that f of x approaches 6 i'm sorry this is approaching negative 6.

01:26 So we say that both the limits are the same.

01:29 That is the left side limit and the right side limits, they are exactly negative 6.

01:34 And this means the limit of if of x and x approaches negative 8 is a negative 6.

01:41 Now let's determine this...

Question

(1) Use the graph of the function f to determine the following limits (a) $\lim_{x \to -5^{-}} f(x)$ (b) $\lim_{x \to 0^{+}} f(x)$ (c) $\lim_{x \to 2^{-}} f(x)$ (d) $\lim_{x \to 2^{+}} f(x)$

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