The function f(x) =(3x+5,if x0

1.	The function f(x) =(3x+5,if x0
Answer» align="ABSMIDDLE" alt="{\bold{\SF{LHS=lim_{x→0^{-}} (3x+5)}}}" CLASS="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%7B%5Cbold%7B%5Csf%7BLHS%3Dlim_%7Bx%E2%86%920%5E%7B-%7D%7D%20%283x%2B5%29%7D%7D%7D" title="{\bold{\sf{LHS=lim_{x→0^{-}} (3x+5)}}}"> ${\bold{\sf{LHS=3(0)+5=5}}}$ ${\bold{\sf{RHS=lim_{x→0^{+}} (12x+5)}}}$ ${\bold{\sf{RHS=12(0)+5=5}}}$ ${\bold{\sf{f(0)=3x+5}}}$ ${\bold{\sf{f(0)=3(0)+5=5}}}$ ${\bold{lim_{x→0^{-}} f(x)=lim_{x→0^{+}} f(x) =f(0) =5}}$ ${\bold{Therefore\:f(x)\:is\:a\:continuous\:function.}}$ ${\bold{\sf{Because,}}}$ ${\bold{\red{lim_{x→a^{-}} f(x)=lim_{x→a^{+}} f(x) =f(a) }}}$ ${\bold{\red{Then \:f(x) \: is \: continuous \:function}}}$

Answer»

align="ABSMIDDLE" alt="{\bold{\SF{LHS=lim_{x→0^{-}} (3x+5)}}}" CLASS="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%7B%5Cbold%7B%5Csf%7BLHS%3Dlim_%7Bx%E2%86%920%5E%7B-%7D%7D%20%283x%2B5%29%7D%7D%7D" title="{\bold{\sf{LHS=lim_{x→0^{-}} (3x+5)}}}">

${\bold{\sf{LHS=3(0)+5=5}}}$