Let f be the function defined by f(x)=2^(x). If five subintervals of equal length are used, what is the value of the left Riemann sum approximation for int_(3)^(5)2^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=2^(x). If five subintervals of equal length are used, what is the value of the left Riemann sum approximation for  int_(3)^(5)2^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Determine Width of Subinterval: Determine the width of each subinterval. The interval from 3 to 5 has a length of 5 - 3 = 2. Since we are using five subintervals of equal length, each subinterval will have a width of 2/5.Identify Left Endpoints: Identify the x-values for the left endpoints of each subinterval. The left endpoints will be at x = 3, 3 + 2/5, 3 + 2*(2/5), 3 + 3*(2/5), and 3 + 4*(2/5). These values are x = 3, 3.4, 3.8, 4.2, and 4.6.Evaluate Function Values: Evaluate the function f(x) = 2^x at each left endpoint. f(3) = 2^3 = 8 f(3.4) = 2^(3.4) ≈ 10.556 f(3.8) = 2^(3.8) ≈ 13.964 f(4.2) = 2^(4.2) ≈ 18.475 f(4.6) = 2^(4.6) ≈ 24.455Calculate Rectangle Areas: Multiply each function value by the width of the subintervals to find the area of each rectangle. The width of each subinterval is 2/5, so we multiply each function value by 2/5: Area1 = f(3) * (2/5) = 8 * (2/5) = 3.2 Area2 = f(3.4) * (2/5) ≈ 10.556 * (2/5) ≈ 4.222 Area3 = f(3.8) * (2/5) ≈ 13.964 * (2/5) ≈ 5.586 Area4 = f(4.2) * (2/5) ≈ 18.475 * (2/5) ≈ 7.39 Area5 = f(4.6) * (2/5) ≈ 24.455 * (2/5) ≈ 9.782Find Riemann Sum: Add the areas of the rectangles to find the left Riemann sum approximation. Left Riemann Sum = Area1 + Area2 + Area3 + Area4 + Area5 ≈ 3.2 + 4.222 + 5.586 + 7.39 + 9.782 ≈ 30.18

Let $f$ be the function defined by $f(x)=2^{x}$ . If five subintervals of equal length are used, what is the value of the left Riemann sum approximation for $\int_{3}^{5} 2^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=2^{x}$ . If five subintervals of equal length are used, what is the value of the left Riemann sum approximation for $\int_{3}^{5} 2^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: