[tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)] = \frac{-1}{3}[/tex], [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
What is Limit?
"A limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value."
We have Limit functions
[tex]\lim_{x \to c} f(x)[/tex] [tex]= \frac{1}{3}[/tex]
[tex]\lim_{x \to c} g(x)[/tex] = [tex]\frac{2}{3}[/tex]
(i) [tex]\lim_{x \to c} [3g(x)] = 3 \lim_{x \to c} [g(x)][/tex]
= [tex]3[/tex] × [tex]\frac{2}{3}[/tex]
= 2
(ii) [tex]\lim_{x \to c}[f(x)+g(x)][/tex]
= [tex]\lim_{x \to c} f(x)+ \lim_{x \to c} g(x)[/tex]
= [tex]\frac{1}{3}-\frac{2}{3}[/tex]
= [tex]\frac{1-2}{3}[/tex]
= [tex]\frac{-1}{3}[/tex]
(iii) [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ][/tex]
= [tex]\frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}[/tex]
= [tex]\frac{\frac{1}{3} }{\frac{2}{3} }[/tex]
= [tex]\frac{1}{2}[/tex]
∴ [tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)][/tex] = [tex]\frac{-1}{3}[/tex] , [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
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