Question

Show work. This is a BC calculus problem.

Answer 1

D.

Explanation:

Recall that the limit definition of a derivative at a point is:

`\displaystyle{(d)/(dx)[f(a)]= f'(a) = \lim_(x \to a)(f(x)-f(a))/(x-a)}`

Hence, if we let f be ln(x + 1) and a be 1, this yields:

`\displaystyle f'(1)= \lim_(x \to 1)(\ln(x+1)-\ln(2))/(x-1)}`

Hence, the limit is equivalent to the derivative of f at x = 1 or f’(1).

In conclusion, our answer is D.