Could someone please solve the questions given below :
Evaluate:
n-->infinity\sum_{r=1}^{n}\frac{r}{4r^2+1}
Prove that if
f(x)=lim\, n--->infinity(x^{1/n}-1)
then f(xy)=f(x)+f(y)
the second questions seems incorrect to me
19for the first one ,,,put it in the form of f(r/n) ....after doing that we get this as
0∫1 (x) / (4x2 + 1)....replacing r/n =x in the equation obtained earlier !
19second one looks a bit funny and really simple if thought simply ;);)
what we know is hat if x,y are independent variables then f(xy) = f(x) + f(y) implies f(x)=klnx or f(x) =0........here it is straightforward that f(x)=0..hence condition satisfied !
