Define the function f(x)= 1, if r = for some integer n 2, otherwise, and consider...

 

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Define the function f(x)= 1, if r = for some integer n 2, otherwise, and consider the integral (2) dr. If A, is the smallest Riemann sum with 71 (equal-width) rectangles and B,, is the largest Riemann sum with n rectangles, prove that lim (B,A,,) = 0. 1-400 f(x) dr. (Hint: combine techniques Conclude that f(x) is integrable on [0, 1] and calculate from the examples we did in class on Friday, January 20.) Define the function f(x)= 1, if r = for some integer n 2, otherwise, and consider the integral (2) dr. If A, is the smallest Riemann sum with 71 (equal-width) rectangles and B,, is the largest Riemann sum with n rectangles, prove that lim (B,A,,) = 0. 1-400 f(x) dr. (Hint: combine techniques Conclude that f(x) is integrable on [0, 1] and calculate from the examples we did in class on Friday, January 20.)