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f(x)=72ln⁡(x) f(x) = 72 \ln(x) for x<0 x < 0 for ∞>0 \infty > 0 Find lim⁡x→+1f(x) \lim_{x \to +1} f(x) . Choose 11 answer:\newline(A) 0 0 \newline(B) 1 1 \newline(C) e e \newline(D) The limit doesn't exist

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Determine end behavior of polynomial and rational functionsright chevron icon

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Q. f(x)=72ln⁡(x) f(x) = 72 \ln(x) for x<0 x < 0 for ∞>0 \infty > 0 Find lim⁡x→+1f(x) \lim_{x \to +1} f(x) . Choose 11 answer:\newline(A) 0 0 \newline(B) 1 1 \newline(C) e e \newline(D) The limit doesn't exist
  1. Function Definition: The function is f(x)=72ln⁡(x)f(x) = 72 \ln(x) for x<0x < 0 and undefined for x≥0x \geq 0.
  2. Approaching Limit: We're looking for the limit as xx approaches 11 from the left, which means we're considering values of xx that are less than 11.
  3. Using Properties of ln(x): Since the natural logarithm function ln⁡(x)\ln(x) is only defined for x>0x > 0, and we're approaching 11 which is greater than 00, we can use the properties of ln⁡(x)\ln(x).
  4. Calculate the Limit: Calculate the limit: lim⁡x→1−72ln⁡(x)\lim_{x\to 1^-} 72 \ln(x).
  5. Approaching ln⁡(1)\ln(1): As xx approaches 11 from the left, ln⁡(x)\ln(x) approaches ln⁡(1)\ln(1), which is 00.
  6. Final Calculation: Therefore, the limit is 72×072 \times 0, which is 00.
  7. Correct Answer: The correct answer is (A) 00.

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