Question

If f(x)=lnx, then lim(x→3)(f(x)-f(3))/(x-3) is?
a) 0
b) 1
c) -1
d) 3

Answer 1

The limit as x approaches 3 of (f(x) - f(3))/(x - 3) is 0.

Step-by-step explanation:

The function f(x) = ln(x) represents the natural logarithm of x. To find the limit as x approaches 3 of (f(x) - f(3))/(x - 3), we can simplify the expression by plugging in the values.

First, we substitute f(x) with ln(x) and f(3) with ln(3), giving us (ln(x) - ln(3))/(x - 3). Next, we can use the property of logarithms that ln(a) - ln(b) = ln(a/b).

So, (ln(x) - ln(3))/(x - 3) simplifies to ln(x/3)/(x - 3). Finally, we can substitute 3 for x in the expression to compute the limit: ln(3/3)/(3 - 3) = ln(1)/0. Since ln(1) = 0, the limit is 0.