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g(x)={[2^(x)-1," for "-8 <= x],[sqrtx," for "x >= 1]:} Find lim_(x rarr4)g(x). Choose 1 answer: (A) 1 (B) 2 (C) 15 (D) The limit doesn't exist.

g(x)={2x−1amp; for −8≤xxamp; for x≥1 g(x)=\left\{\begin{array}{ll} 2^{x}-1 &amp; \text { for }-8 \leq x \\ \sqrt{x} &amp; \text { for } x \geq 1 \end{array}\right. \newlineFind lim⁡x→4g(x) \lim _{x \rightarrow 4} g(x) .\newlineChoose 11 answer:\newline(A) 11\newline(B) 22\newline(C) 15 \mathbf{1 5} \newline(D) The limit doesn't exist.

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Q. g(x)={2x−1 for −8≤xx for x≥1 g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right. \newlineFind lim⁡x→4g(x) \lim _{x \rightarrow 4} g(x) .\newlineChoose 11 answer:\newline(A) 11\newline(B) 22\newline(C) 15 \mathbf{1 5} \newline(D) The limit doesn't exist.
  1. Determine piecewise function for xx approaching 44: We need to determine which piece of the piecewise function g(x)g(x) applies when xx is approaching 44. The function g(x)g(x) is defined as 2x−12^{x}-1 for x≤−8x \leq -8 and as x\sqrt{x} for x≥1x \geq 1. Since 44 is greater than 4411, we will use the x\sqrt{x} part of the function to find the limit as xx approaches 44.
  2. Calculate limit of x\sqrt{x} as xx approaches 44: Now we calculate the limit of x\sqrt{x} as xx approaches 44. The limit of a square root function is the square root of the limit point, provided the limit point is within the domain of the function. Since 44 is within the domain of x\sqrt{x}, we can directly substitute xx with 44.
  3. Substitute xx with 44 in x\sqrt{x} to find limit: Substituting xx with 44 in x\sqrt{x} gives us 4\sqrt{4}, which equals 22. Therefore, the limit of g(x)g(x) as xx approaches 44 is 22.

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