Which of the following is true If `lim_(x->a) f(x)->0,lim_(x->a)g(x)->0,lim_(x->a)h(x)->oo`

Let f(x)=x+sqrt(x^2+2x) and g(x)=sqrt(x^2+2x-x) , then which of the following is/are true. a. lim_(x->oo)g(x)=1 b. lim_(x->oo)f(x)=1 c. lim_(x->oo)f(x)=-1 d. lim_(x->oo)g(x)=-1

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.

Which of the following limits does not exist ?(a) lim_(x->oo) cosec^(-1) (x/(x+7) (B) lim_(x->1) sec^(-1) (sin^(-1)x) (C) lim_(x->0^+) x^(1/x) (D) lim_(x->0) (tan(pi/8+x))^(cotx)

If alpha in(0,1) and f:R->R and lim_(x->oo)f(x)=0,lim_(x->oo)(f(x)-f(alphax))/x=0, then lim_(x->oo)f(x)/x=lambda where 2lambda+7 is

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

If lim_(x->a)[f(x)g(x)] exists, then both lim_(xtoa)f(x) and lim_(x->a)g(x) exist.

lim_(x rarr oo)(1)/(x)=0

Consider the function f(x)={(max(x,(1)/(x)))/(min(x,(1)/(x))),quad if x!=0 and 1,quad if x=0 then lim_(x rarr0){f(x)}+lim_(x rarr1){f(x)},lim_(x rarr1)[f(x)]=