(x+(1)/(x))^(x)+x^((1+1/x))

Find (dy)/(dx):y=(x+(1)/(x))^x+(x+(1)/(x))^(1/x)

If y=(1+(1)/(x))^(x), then (dy)/(dx)=(1+(1)/(x))^(x){log(1+(1)/(x))-(1)/(x+1)}(b)(1+(1)/(x))^(x)log(1+(1)/(x))(c)(x+(1)/(x))^(x){log(x+1)-(x)/(x+1)}(d)(x+(1)/(x))^(x){log(1+(1)/(x))+(1)/(x+1)}

if f(x)=(x)/((1+x))+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+. . . infinite terms , Discuss continuity at x=0

Evaluate lim_(x rarr oo)[(x+1)^((x+2)/(x+1))-x^((x+1)/(x))]

f(x)={(x)/(1+x)+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+....n terms} and x gt 0 then Lt_(x to oo)f(x)=

f(x)=[(x)/(1+x)+(x)/((1+x)(1+2x))+...+(x)/((1+9x)(1+10x))] then the value of the integral int_(-5)^(5)(f(x)+(1)/(1+10x))dx is

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)),x>1

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)), x gt 1 . Then