Let `f(x)={(1+3x)^(1/x),x!=0e^3,x=0dotD i s c u s st h econ t inu i t yof` `f(x)` at `(a)x=0,` (b) `x=1.`

Let f(x)={(1+3x)^((1)/(7)),x!=0e^(3),x=0 Discuss the continuity of f(x) at (a) x=0 (b) x=1

Let f(x)={[((e^(3x)-1))/(x),,x!=0],[3,,x=0]} then 2f'(0) is

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(ax+bx^(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)_(e)3

Let f(x)=x^(5)[1/(x^(3))],x!=0 & f(0)=0 (where [.] represent G.I.F.), Then lim_(xto0)f(x)

Let f(x)=x^(3)-x^(2)-x+1 and g(x)={max{f(t);0<=t<=x},0<=x<=1,3-x,1<=x<=2 Discuss the continuity and differentiability of the function g(x) in the interval (0,2).

If f(x)=1+3int_(0)^(x)t^(2)f(t)dt, then the number of solution of f(x)=x^(2)+1 is