Question

Use L'Hopital's rule to determine the following limit, where a is a

positive constant value lim (x+a) ln (x+a)

Answer 1

Answer: -∞

E

use L'Hopital's rule, we need to take the derivative of both the numerator and denominator separately.

lim (x+a) ln (x+a)

= lim (ln (x+a) / 1/(x+a))

Now taking the derivative of both the numerator and denominator:

= lim ((1/(x+a)) / (-1/(x+a)^2))

= lim (-x-a)

As x approaches infinity, the limit equals negative infinity.

Therefore, the answer is -∞.