`lim_(x->1) (nx^(n+1)-nx^(n)+1)/((e^x-e^2)sinpix)`

lim_(xto1) (nx^(n-1)-(n+1)x^(n)+1)/((e^(x)-e)sinpix) , where n=100 ,is equal to

lim_(x rarr1)(nx^(n+1)-(n+1)x^(n)+1)/((e^(x)-e)sin pi x), where n=100, is equal to :(5050)/(pi e) (b) (100)/(pi e)(c)-(5050)/(pi e) (d) -(4950)/(pi e)

lim_(x->oo)(1-x+x.e^(1/n))^n

The value of lim_(x rarr oo)(x^(n)+nx^(n-1)+1)/(e^(|x|)),n in1 is

int(e^(x)(1-nx^(n-1)-x^(2n)))/((1-x^(n)) sqrt(1-x^(2n)))d=....+c

Evaluate: int e^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n)))dx

Let lim_(n->oo)((x^2+2x+3+sinpix)^n-1)/((x^2+2x+3+sinpix)^n+1) . then

Let f(x)=lim_(nrarroo)((x^(2)+2x+4+sinpix^(n))-1)/((x^(2)+2x+4+sinpix^(n))+1) , then

Show that 1+2x + 3x^2 +….+ nx^(n-1) = (1-(n+1)x^(n) + nx^(n+1))/((1-x)^2) for all n in N .

if f(x) = lim_(n->oo) 2/n^2(sum_(k=1)^n kx)((3^(nx)-1)/(3^(nx)+1)) where n in N , then find the sum of all the solution of the equation f(x) = |x^2 - 2|