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g(x)={[2^(x)-1," for "-8 <= x < 1],[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)={2x1amp; for 8xlt;1xamp; for x1 g(x)=\left\{\begin{array}{ll} 2^{x}-1 &amp; \text { for }-8 \leq x&lt;1 \\ \sqrt{x} &amp; \text { for } x \geq 1 \end{array}\right. \newlineFind limx4g(x) \lim _{x \rightarrow 4} g(x) .\newlineChoose 11 answer:\newline(A) 11\newline(B) 22\newline(C) 1515\newline(D) The limit doesn't exist.

Full solution

Q. g(x)={2x1 for 8x<1x for x1 g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x<1 \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right. \newlineFind limx4g(x) \lim _{x \rightarrow 4} g(x) .\newlineChoose 11 answer:\newline(A) 11\newline(B) 22\newline(C) 1515\newline(D) The limit doesn't exist.
  1. Determine Piecewise Function: Determine which piece of the piecewise function to use for the limit as xx approaches 44.\newlineSince 44 is greater than 11, we will use the second piece of the function, which is g(x)=xg(x) = \sqrt{x} for x1x \geq 1.
  2. Calculate Limit of g(x)g(x): Calculate the limit of g(x)g(x) as xx approaches 44 using the appropriate piece.limx4g(x)=limx4x=4\lim_{x \to 4} g(x) = \lim_{x \to 4} \sqrt{x} = \sqrt{4}
  3. Evaluate Square Root: Evaluate the square root of 44 to find the limit.4=2\sqrt{4} = 2

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