Question

11:50AU Mon Ape 22 Mon Ape 22 webasionnet The graph of a function \( g \) is shown. (1) Use it to state the values (is they exigt) of the following: (a) \( \lim _{x \rightarrow 2^{-}} g(x) \) (b) \( \lim _{x \rightarrow 2^{*}} g(x) \) (c) \( \lim _{x \rightarrow 2} g(x) \) (d) \( \lim _{x \rightarrow 5^{-}} g(x) \) (e) \( \lim _{x \rightarrow 5^{+}} g(x) \) (f) \( \lim _{x \rightarrow 5} 9(x) \) Solution Looking at the graph we see that the values of \( g(x) \) approach \( \square \) as \( x \) approaches 2 from the left, but they approach \( \square \) as \( x \) approaches 2 from the right. Therefore \( (a) \lim _{x \rightarrow 2^{-}} g(x)= \) \( \square \) and (b) \( \lim _{x \rightarrow 2^{+}} g(x)= \) \( \square \) Since the left and right limits are different, we conclude that (c) the limit as \( x \) approaches 2 of \( g(x) \) does not exist. The graph also shows that (d) \( \lim _{x \rightarrow 5^{-}} g(x)= \) \( \square \) and (e) \( \lim _{x \rightarrow 5^{+}} g(x)= \) \( \square \) This time, the left and right limits are the same and so, by this theorem, we have (f) \( \lim _{x \rightarrow 5} g(x)= \) \( \square \) Despite this tact, notice that \( g(5)+2 \). Nead Heln? Dout:

          11:50AU Mon Ape 22
Mon Ape 22
webasionnet
The graph of a function \( g \) is shown.
(1)
Use it to state the values (is they exigt) of the following:
(a) \( \lim _{x \rightarrow 2^{-}} g(x) \)
(b) \( \lim _{x \rightarrow 2^{*}} g(x) \)
(c) \( \lim _{x \rightarrow 2} g(x) \)
(d) \( \lim _{x \rightarrow 5^{-}} g(x) \)
(e) \( \lim _{x \rightarrow 5^{+}} g(x) \)
(f) \( \lim _{x \rightarrow 5} 9(x) \)

Solution
Looking at the graph we see that the values of \( g(x) \) approach \( \square \) as \( x \) approaches 2 from the left, but they approach \( \square \) as \( x \) approaches 2 from the right. Therefore \( (a) \lim _{x \rightarrow 2^{-}} g(x)= \) \( \square \) and (b) \( \lim _{x \rightarrow 2^{+}} g(x)= \) \( \square \)
Since the left and right limits are different, we conclude that (c) the limit as \( x \) approaches 2 of \( g(x) \) does not exist.
The graph also shows that (d) \( \lim _{x \rightarrow 5^{-}} g(x)= \) \( \square \) and
(e) \( \lim _{x \rightarrow 5^{+}} g(x)= \) \( \square \)
This time, the left and right limits are the same and so, by this theorem, we have (f) \( \lim _{x \rightarrow 5} g(x)= \) \( \square \)
Despite this tact, notice that \( g(5)+2 \).
Nead Heln? Dout:

11:50AU Mon Ape 22
Mon Ape 22
webasionnet
The graph of a function g is shown.
(1)
Use it to state the values (is they exigt) of the following:
(a) limx → 2^- g(x)
(b) limx → 2^* g(x)
(c) limx → 2 g(x)
(d) limx → 5^- g(x)
(e) limx → 5^+ g(x)
(f) limx → 5 9(x)

Solution
Looking at the graph we see that the values of g(x) approach □ as x approaches 2 from the left, but they approach □ as x approaches 2 from the right. Therefore (a) limx → 2^- g(x)= □ and (b) limx → 2^+ g(x)= □
Since the left and right limits are different, we conclude that (c) the limit as x approaches 2 of g(x) does not exist.
The graph also shows that (d) limx → 5^- g(x)= □ and
(e) limx → 5^+ g(x)= □
This time, the left and right limits are the same and so, by this theorem, we have (f) limx → 5 g(x)= □
Despite this tact, notice that g(5)+2.
Nead Heln? Dout:

Added by April V.

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