Question

For which value C is the function CLEAR STEP BY STEP is App RECIATED SC. (x+2)/3 if so if > O'. continuous at 0. Justify your answer.

Answer 1

Suppose A=(x)* applying logoritms both sides, we get In A = ln(x) = xin x (:+In (**) = nin x) In x lim In A=lim X-0 x+0 1 1 X x =lim x0 * x2 8 -, by using L'hospital's rule :: lim =lim g(x) x? = lim(-x) = 0 Therefore lim In A=0= In (lim A)=0=lim A= e = 1=lim(x)* = 1 x0 x=0 1 a face Given that f (x) if xs0 if x>0 lim | (x )= lim (**) = 1, by (i) lim f (x)= limc(x+2)} = c(0+2)} = c(2); Since f is continuous at x = 0 So that lim /(x) = lim x(x)= f (0) 1 x=0 X+0 80 1 Therefore c(2)3 =1=c= 123