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Find lim_(x rarr3)f(x) for f(x)=(x^(2)-4)/(11-2x).

Find lim⁡x→3f(x) \lim _{x \rightarrow 3} f(x) for f(x)=x2−411−2x f(x)=\frac{x^{2}-4}{11-2 x} .

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Full solution

Q. Find lim⁡x→3f(x) \lim _{x \rightarrow 3} f(x) for f(x)=x2−411−2x f(x)=\frac{x^{2}-4}{11-2 x} .
  1. Substitute xx into function: Substitute the value of xx into the function to see if the function is defined at that point.\newlineLet's substitute x=3x = 3 into f(x)=x2−411−2xf(x) = \frac{x^2 - 4}{11 - 2x}.\newlinef(3)=(3)2−411−2⋅3f(3) = \frac{(3)^2 - 4}{11 - 2\cdot 3}\newlinef(3)=9−411−6f(3) = \frac{9 - 4}{11 - 6}\newlinef(3)=55f(3) = \frac{5}{5}\newlinef(3)=1f(3) = 1
  2. Calculate f(3)f(3): Since the function is defined at x=3x = 3 and there is no indeterminate form, the limit as xx approaches 33 is simply the value of the function at x=3x = 3. Therefore, lim⁡x→3f(x)=f(3)=1\lim_{x \to 3}f(x) = f(3) = 1.

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