Given-a-function-f-x-2x-a-x-lt-3-ax-b-3-x-3-b-5x-x-gt-3-find-the-value-of-a-and-b-such-that-lim-x-3-f-x-and-lim-x-3-f-x-exist-

Question Number 99340 by bobhans last updated on 20/Jun/20

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{2x}−\mathrm{a}\:,\:\mathrm{x}<−\mathrm{3}}\\{\mathrm{ax}+\mathrm{b}\:,\:−\mathrm{3}\leqslant\mathrm{x}\leqslant\mathrm{3}}\\{\mathrm{b}−\mathrm{5x}\:,\:\mathrm{x}>\mathrm{3}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}f}\left(\mathrm{x}\right)\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{exist}\: \\ $$

Commented by PRITHWISH SEN 2 last updated on 20/Jun/20

$$\mathrm{3a}+\mathrm{b}=\mathrm{b}−\mathrm{15}\Rightarrow\mathrm{a}=−\mathrm{5} \\ $$$$−\mathrm{6}+\mathrm{5}=\mathrm{15}+\mathrm{b}\Rightarrow\mathrm{b}=−\mathrm{16}\:\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}} \\ $$

Commented by bobhans last updated on 20/Jun/20

$$\mathrm{thank}\:\mathrm{you} \\ $$

Commented by PRITHWISH SEN 2 last updated on 20/Jun/20

$$\mathrm{welcome} \\ $$

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