A function `f: RvecR` is defined as `f(x)=(lim)_(nvecoo)(a x^2+b x+c+e^(n x))/(1+c.e^(n x))` is continuous on `R` then find the values of a,b,c.

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

Find the values of a if f(x)=("lim")_(n rarr oo)(a x^(2n)+2)/(x^(2n)+a+1) is continuous at x=1.

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

Evaluate : ("lim")_(xvecoo)(a x^2+b x+c)/(dx^2+e x+f)dot

Evaluate : ("lim")_(xvecoo)(a x^2+b x+c)/(dx^2+e x+f)dot

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x^3)/(x^2))^(1/x),x >0 is continuous at x=0, then a=0 b. b=e^3 c. a=1 d. b=(log)_e3

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to (a) 2 (b) 1 (c) 1/2 (d) 0

If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given by g(x)=x/(x-1) . Find foga n dgofdot

If f(x)=lim_(nrarroo)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1)f(x) exists, then The value of b is