Let F(x) = 5x - 4, 0

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIApplied Mathematicslimit of a functionQuestionLet $$f(x)=\begin{cases} 5x-4, 0<x\le 1 \\ 4x^{3}-3x,1<x<2 \end{cases}$$.Find $$\displaystyle\lim_{x\rightarrow 1}f(x)$$.Open in AppSolutionVerified by Toppr

$$\displaystyle\lim_{x\rightarrow 1^{+}}f(x)=\lim_{h\rightarrow 0}f(1+h)=\lim_{h\rightarrow 0}[4(1+h)^{3}-3(1+h)]=(4\times 1^{3}-3)=1$$$$\displaystyle\lim_{x\rightarrow 1^{-}}f(x)=\lim_{h\rightarrow 0}f(1-h)_=\lim_{h\rightarrow 0}[5(1-h)-4]=(5-4)=1$$$$\therefore\displaystyle\lim_{x\rightarrow 1^{+}}f(x)=\lim_{x\rightarrow 1^{-}}f(x)=1$$ and do $$\displaystyle\lim_{x\rightarrow 1}f(x)=1$$

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Check the continuity of

f(x)={(1+3x)1/xx≠0e3x=0

at x=0.

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