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Let f(x)=(3)/(x). Select the correct description of the one-sided limits of f at x=0. Choose 1 answer: (A) lim_(x rarr0^(+))f(x)=+oo and lim_(x rarr0^(-))f(x)=+oo (B) lim_(x rarr0^(+))f(x)=+oo and lim_(x rarr0^(-))f(x)=-oo (c) lim_(x rarr0^(+))f(x)=-oo and lim_(x rarr0^(-))f(x)=+oo (D) lim_(x rarr0^(+))f(x)=-oo and lim_(x rarr0^(-))f(x)=-oo

Let f(x)=3x f(x)=\frac{3}{x} .\newlineSelect the correct description of the one-sided limits of f f at x=0 x=0 .\newlineChoose 11 answer:\newline(A) lim⁡x→0+f(x)=+∞ \lim _{x \rightarrow 0^{+}} f(x)=+\infty and lim⁡x→0−f(x)=+∞ \lim _{x \rightarrow 0^{-}} f(x)=+\infty \newline(B) lim⁡x→0+f(x)=+∞ \lim _{x \rightarrow 0^{+}} f(x)=+\infty and lim⁡x→0−f(x)=−∞ \lim _{x \rightarrow 0^{-}} f(x)=-\infty \newline(C) lim⁡x→0+f(x)=−∞ \lim _{x \rightarrow 0^{+}} f(x)=-\infty and lim⁡x→0−f(x)=+∞ \lim _{x \rightarrow 0^{-}} f(x)=+\infty \newline(D) lim⁡x→0+f(x)=−∞ \lim _{x \rightarrow 0^{+}} f(x)=-\infty and lim⁡x→0−f(x)=−∞ \lim _{x \rightarrow 0^{-}} f(x)=-\infty

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Q. Let f(x)=3x f(x)=\frac{3}{x} .\newlineSelect the correct description of the one-sided limits of f f at x=0 x=0 .\newlineChoose 11 answer:\newline(A) lim⁡x→0+f(x)=+∞ \lim _{x \rightarrow 0^{+}} f(x)=+\infty and lim⁡x→0−f(x)=+∞ \lim _{x \rightarrow 0^{-}} f(x)=+\infty \newline(B) lim⁡x→0+f(x)=+∞ \lim _{x \rightarrow 0^{+}} f(x)=+\infty and lim⁡x→0−f(x)=−∞ \lim _{x \rightarrow 0^{-}} f(x)=-\infty \newline(C) lim⁡x→0+f(x)=−∞ \lim _{x \rightarrow 0^{+}} f(x)=-\infty and lim⁡x→0−f(x)=+∞ \lim _{x \rightarrow 0^{-}} f(x)=+\infty \newline(D) lim⁡x→0+f(x)=−∞ \lim _{x \rightarrow 0^{+}} f(x)=-\infty and lim⁡x→0−f(x)=−∞ \lim _{x \rightarrow 0^{-}} f(x)=-\infty
  1. Analyze behavior of f(x)f(x) as xx approaches 0+0+: Analyze the behavior of the function f(x)=3xf(x) = \frac{3}{x} as xx approaches 00 from the positive side (x→0+x \rightarrow 0^+).\newlineAs xx gets closer to 00 from the positive side, the value of f(x)f(x) becomes larger and larger because the denominator of the fraction is getting smaller. This means that the function is approaching positive infinity.
  2. Calculate limit of f(x)f(x) as xx approaches 0+0+: Calculate the limit of f(x)f(x) as xx approaches 00 from the positive side.\newlinelim⁡x→0+f(x)=lim⁡x→0+(3x)=+∞\lim_{x \to 0^+} f(x) = \lim_{x \to 0^+} \left(\frac{3}{x}\right) = +\infty
  3. Analyze behavior of f(x)f(x) as xx approaches 0−0-: Analyze the behavior of the function f(x)=3xf(x) = \frac{3}{x} as xx approaches 00 from the negative side (x→0−x \rightarrow 0^-).\newlineAs xx gets closer to 00 from the negative side, the value of f(x)f(x) becomes more negative and larger in magnitude because the denominator of the fraction is getting smaller and is negative. This means that the function is approaching negative infinity.
  4. Calculate limit of f(x)f(x) as xx approaches 0−0-: Calculate the limit of f(x)f(x) as xx approaches 00 from the negative side.\newlinelim⁡x→0−f(x)=lim⁡x→0−(3x)=−∞\lim_{x \to 0^-} f(x) = \lim_{x \to 0^-} \left(\frac{3}{x}\right) = -\infty
  5. Combine results from Step 22 and Step 44: Combine the results from Step 22 and Step 44 to answer the question prompt.\newlineThe one-sided limits of the function f(x)=3xf(x) = \frac{3}{x} as xx approaches 00 are:\newlinelim⁡x→0+f(x)=+∞\lim_{x \to 0^+} f(x) = +\infty and lim⁡x→0−f(x)=−∞\lim_{x \to 0^-} f(x) = -\infty

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