Are these two limits exist? How to prove?
1.)lim x-->∞ (sqrt(x^2 + x)) - sqrt(x^2 - dx)
where d is a positive constant
2.)limx-->9 (xsqrt(x)-3)/(x-9)
The first one exists:
.
The second one doesn't exist as the numerator tends to a finite value and the denominator tends to 0. Division by zero is undefined.
