Final Answer
$\frac{1}{9}$
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Step-by-step Solution
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1
Calculating the natural logarithm of $3$
$\lim_{x\to3}\left(\left(\frac{\ln\left(x\right)-\ln\left(3\right)}{x-3}\right)^2\right)$
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$\lim_{x\to3}\left(\left(\frac{\ln\left(x\right)-\ln\left(3\right)}{x-3}\right)^2\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of ((ln(x)-ln(3))/(x-3))^2 as x approaches 3. Calculating the natural logarithm of 3. Multiply -1 times \ln\left(3\right). Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. If we directly evaluate the limit \lim_{x\to 3}\left(\frac{\ln\left(x\right)-\ln\left(3\right)}{x-3}\right) as x tends to 3, we can see that it gives us an indeterminate form.
Final Answer
$\frac{1}{9}$
Exact Numeric Answer
$0.1111$