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Find lim_(x rarr-1)(x^(2)-9)/(x^(2)+1). Choose 1 answer: (A) -4 (B) -5 (C) -9 (D) The limit doesn't exist

Find lim⁡x→−1x2−9x2+1 \lim _{x \rightarrow-1} \frac{x^{2}-9}{x^{2}+1} .\newlineChoose 11 answer:\newline(A) −4-4\newline(B) −5-5\newline(C) −9-9\newline(D) The limit doesn't exist

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Q. Find lim⁡x→−1x2−9x2+1 \lim _{x \rightarrow-1} \frac{x^{2}-9}{x^{2}+1} .\newlineChoose 11 answer:\newline(A) −4-4\newline(B) −5-5\newline(C) −9-9\newline(D) The limit doesn't exist
  1. Substitute x value: Substitute the value of xx approaching −1-1 into the function to see if the function is defined at that point.\newlinelim⁡x→−1x2−9x2+1=(−1)2−9(−1)2+1\lim_{x \to -1}\frac{x^2 - 9}{x^2 + 1} = \frac{(-1)^2 - 9}{(-1)^2 + 1}
  2. Perform calculations: Perform the calculations for the numerator and the denominator separately.\newlineNumerator: (−1)2−9=1−9=−8(-1)^2 - 9 = 1 - 9 = -8\newlineDenominator: (−1)2+1=1+1=2(-1)^2 + 1 = 1 + 1 = 2
  3. Find the limit: Divide the calculated numerator by the calculated denominator to find the limit.\newlineLimit: −8/2=−4-8 / 2 = -4

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