Find \( \lim\limits_{x \to 0}f(x)\) and \( \lim\limits_{x \to 1}f(x)\) where \( f(x)=\{2x+3,x≤0,3(x+1),x>0 \)

Asked by Abhisek | 1 year ago |  99

1 Answer

Solution :-

\( \lim\limits_{x \to 0^-}f(x)= \lim\limits_{x \to 0}[2x+3]\)

\( 2(0)+3=3\)

\( \lim\limits_{x \to 0^+}f(x)= \lim\limits_{x \to 0}3(x+1)\)

\( 3(0+1)=3\)

\( \lim\limits_{x \to 0^-}f(x)= \lim\limits_{x \to 0^+}f(x)= \lim\limits_{x \to 0}f(x)=3\)

\( \lim\limits_{x \to 1^-}f(x)= \lim\limits_{x \to 1}(x+1)=3(1+1)=6\)

\( \lim\limits_{x \to 1^+}f(x)= \lim\limits_{x \to 1^-}f(x)= \lim\limits_{x \to 1}f(x)=6\)

Answered by Pragya Singh | 1 year ago

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