If `f(x)=(3x^2+a x+a+1)/(x^2+x-2),` then which of the following can be correct
(a) `("lim")_(x-> 1)f(x) for a=-2` (b) `("lim")(x->-2)f(x) for a=13` (c) `("lim")(x-> 1)f(x)=4/3` (d) `("lim")(x->-2)f(x)=-1/3`

If f(x)=(x^(2)-3x+2)/(x^(2)-7x+12), then which of the following limits exists? (i)lim_(xtooo) sin^(-1)f(x)" "(ii)lim_(xtooo) cos^(-1)f(x)

Consider the following graph of the function y=f(x). Which of the following is//are correct? (a) lim_(xto1) f(x) does not exist. (b) lim_(xto2)f(x) does not exist. (c) lim_(xto3) f(x)=3. (d)lim_(xto1.99) f(x) exists.

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (A) ("lim")_(x->5)f(x)=1 (B) ("lim")_(x->5)f(x)=0 (C) ("lim")_(x->5)f(x) does not exist. (D)none of these

If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")_(xrarrpi/2)f(x)=-oo (b) ("lim")_(xrarrpi/2)f(x)=oo (c) ("lim")_(xrarrpi/2)f(x)=0 (d) none of these

Find ("lim")_(xto2)(xf(2)-2f(x))/(x-2) if f(2)=4 and f′(2)=1

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2) sqrt({x}cot{x}),for x 0 Where [x] is the integral part and {x} is the fractional part of x , then ("lim")_(xvec0^+)f(x)=1 , ("lim")_(xvec0^-)f(x)=cot1 , cot^(-1)(("lim")_(xvec0^-)f(x))^2=1 , tan^(-1)(("lim")_(xvec0^+)f(x))=pi/4

Let f(x)=(bx+a)/(x+1), lim_(x to 0)f(x)=2 then the value of a is .

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(x i)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)

If f(x)=sqrt((x-sinx)/(x+cos^2x)) , then lim_(x rarr infty)f(x) is