If `lim_(x to a)f(x)=lim_(x to a)phi(x)` then always `f(x)=phi(x)`. Is it true for all cases. Explain.

If int_(a)^(b)f(x)dx=int_(a)^(b)phi(x)dx , then-

if lim_(xrarra)f(x)=lim_(xrarra)g(x) ,then whether f(x)=g(x) is always true?Justify your answer by an example

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then f has

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)xg(x)) lim_(xto0)((x-1+cosx)/x)^(1/x) is equal to

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

Does underset(xrarra)"lim"f(x)=underset(xrarra)"lim"phi(x) "always imply" f(x)=phi(x) ? Justify your answer .

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 underset(x rarr a)lim f(x) = underset(x rarr a)lim g(x) , then whether f(x) = g(x) is always true ? Justify your answer by an example.

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).