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If f(x)=ln x, then lim_(x rarr3)(f(x)=f(3))/(x-3) is

If f(x)=ln⁡x f(x)=\ln x , then lim⁡x→3f(x)=f(3)x−3 \lim _{x \rightarrow 3} \frac{f(x)=f(3)}{x-3} is

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Full solution

Q. If f(x)=ln⁡x f(x)=\ln x , then lim⁡x→3f(x)=f(3)x−3 \lim _{x \rightarrow 3} \frac{f(x)=f(3)}{x-3} is
  1. Identify Problem Type: Identify the type of limit problem we're dealing with.
  2. Recall Derivative Definition: Recall the definition of the derivative of ff at a point aa.
  3. Apply Definition to ln⁡x\ln x: Apply the definition of the derivative to f(x)=ln⁡xf(x) = \ln x at x=3x = 3.
  4. Calculate ln⁡x\ln x Derivative: Calculate the derivative of f(x)=ln⁡xf(x) = \ln x.
  5. Evaluate at x=3x = 3: Evaluate the derivative at x=3x = 3.
  6. Realize Limit is Derivative: Realize that the limit we're trying to find is the same as the derivative of ln⁡x\ln x at x=3x = 3.

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