Question

( f(x)=left{begin{array}{cc}frac{1}{1 / x+1} & , x eq 0 0 & x=0end{array}right. )
(a) ( lim _{x rightarrow 0^{-}}left(frac{1}{x}right)=-infty )
( lim _{x rightarrow 0^{-}} e^{y x}=0 Rightarrow lim _{x rightarrow 0^{-}} frac{1}{e^{y_{x+1}}}=frac{1}{1} )
( (b) mid lim _{x rightarrow 0^{+}}left(frac{1}{x}right)=infty )
( S )
( lim _{x rightarrow 0^{+}} e^{y x}=infty Rightarrow lim _{x rightarrow 0^{+}} frac{1}{e^{x} x+1}=0 )
( fleft(lim _{x rightarrow 0^{+}} f(x) eq lim _{x rightarrow 0^{-}} f(x) eq f(0)right. )
So dis continuour
( f(7) ) is dis continuas

# .x) = lim f(x) NG) f(x) is continuous at x = 1 (D) f(x) is continuous at x = 1 and 3 (B) f(x) is continuous at x mul statement is - X- 3 2. If f(x) = e/*+1 O : * 870 then - then - (A) lim f(x)=1 X=0 (C) f(x) is discontinuous at x = 0 If function f(x) = - J1+x - 3/1+x - (B) lim f(x) = 0 (D) f(x) is continuous (A) 2 is continuous function, then f(0) is equal to - (B) 1/4 f(x) = 12 (a + 2)x +2a (C) 1/6 8-2 X*2 (D) 11 is continuous at x = 2, then a is equal to - X = 2 (B)1 log(1 + 2ax) -log(1 - bx) (0) -1 X70 (D) 2

Solution