The correct options are A lim_x→ 1^ g(x)=1 B lim_x→ 1^+g(x)=1 C lim_x→ 4^ g(x)=4 As #160; #160; x→ 1^ , g(x)=x^2⇒lim_x→ 1^ g(x)=1 As ...

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Continuity of a Function

gx= x2 x< 1 ...

Question

$g (x) = ⎧ ⎨ ⎩ \begin{matrix} x^{2} & for x < 1 x & for 1 < x < 4 4 - x & for x > 4 \end{matrix}$
Then

lim x \to 1^{-} g (x) = 1

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lim x \to 1^{+} g (x) = 1

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lim x \to 4^{-} g (x) = 4

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lim x \to 4^{+} g (x) = 4

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Solution

The correct options are
A $lim x \to 1^{-} g (x) = 1$
B $lim x \to 1^{+} g (x) = 1$
C $lim x \to 4^{-} g (x) = 4$
As $x \to 1^{-}, g (x) = x^{2} \Rightarrow lim x \to 1^{-} g (x) = 1$
As $x \to 1^{+}, g (x) = x \Rightarrow lim x \to 1^{+} g (x) = 1$

As $x \to 4^{-}, g (x) = x \Rightarrow lim x \to 4^{-} g (x) = 4$
As $x \to 4^{+}, g (x) = 4 - x \Rightarrow lim x \to 4^{+} g (x) = 0$

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