n→∞limn1∫1nx+1x−1dx
My approach is not correct, I think.
I took f(x)=(x-1)/(x+1) which is continuous so there is a F(x) a primitive of f(x) such that F'(x)=f(x)
So I used L'Hospital but when I derived, I derived for n which is number, not for x and I think it's not correct.
I obtained n→∞limnF(n)−F(1)=n→∞limf(n)=1 which is the correct answer but I'm not sure if this is the right method.There's another way to solve this?
My approach is not correct, I think.
I took f(x)=(x-1)/(x+1) which is continuous so there is a F(x) a primitive of f(x) such that F'(x)=f(x)
So I used L'Hospital but when I derived, I derived for n which is number, not for x and I think it's not correct.
I obtained n→∞limnF(n)−F(1)=n→∞limf(n)=1 which is the correct answer but I'm not sure if this is the right method.There's another way to solve this?