If `("lim")_(xtoa)[f(x)g(x)]` exists, then both `("lim")_(xtoa)f(x)a n d("lim")_(xtoa)g(x)` exist.

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

lim_(xtoa)(x^(2)sinx-a^(2)sina)/(x-a)

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")_(xvec5)f(x)=1 (b) ("lim")_(xvec5)f(x)=0 (c) ("lim")_(xvec5)f(x)does not exist (d)none of these

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest integer function, then (a) ("lim")_(xvec0)[f(x)]=0 (b) ("lim")_(xvec0)[f(x)]=1 (c) ("lim")_(xvec0)[(f(x))/x] does not exist (d) ("lim")_(xvec0)[(f(x))/x] exists

If f(x)={(x^nsin(1/(x^2)),x!=0), (0,x=0):} , (n in I) , then (a) lim_(xrarr0)f(x) exists for n >1 (b) lim_(xrarr0)f(x) exists for n<0 (c) lim_(xrarr0)f(x) does not exist for any value of n (d) lim_(xrarr0)f(x) cannot be determined

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

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)=o (d) none of these