Consider the function f(x)= on the interval 0 x 2. (a) Sketch the graph...

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Consider the function f(x)=³ on the interval 0 ≤ x ≤ 2. (a) Sketch the graph of y = f(x) with n = 4 rectangles on the interval [0, 2] using a right endpoint approximation. Calculate the value of R₁. Do you think this is an overestimate (too high) or an underestimate (too low) of the true value of the area under the graph on this interval? Why? (b) Sketch the graph of y = f(r) on the interval [0, 2] again, but this time with n = 5 rectangles using a left endpoint approximation. Calculate the value of L5. Do you think this is an overestimate or an underestimate of the true area under the graph on this interval? Why? (c) Find and simplify the expression for R₁, in terms of n. You will find the following formula useful: n² (n + 1)² 4 (d) Find the exact value of fff(x)de by calculating the limit of R, as n goes to infinity. Consider the function f(x)=³ on the interval 0 ≤ x ≤ 2. (a) Sketch the graph of y = f(x) with n = 4 rectangles on the interval [0, 2] using a right endpoint approximation. Calculate the value of R₁. Do you think this is an overestimate (too high) or an underestimate (too low) of the true value of the area under the graph on this interval? Why? (b) Sketch the graph of y = f(r) on the interval [0, 2] again, but this time with n = 5 rectangles using a left endpoint approximation. Calculate the value of L5. Do you think this is an overestimate or an underestimate of the true area under the graph on this interval? Why? (c) Find and simplify the expression for R₁, in terms of n. You will find the following formula useful: n² (n + 1)² 4 (d) Find the exact value of fff(x)de by calculating the limit of R, as n goes to infinity.

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a To sketch the graph of y fx with n 4 rectangles on the interval 02 using a right endpoint approximation we first need to find the width of each rect... View the full answer