1 2 3 4 5 2 -1 -2 3 S(x) The function f is continuous on the closed interval [0,6]and has values as shown in the table above. Using the intervals [0,2], [2,4], and [4,6], what is the approximation of midpoint Riemann sum? Jo (*)ax obtained from a
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- (a) Sketch the graph of the function on the given interval. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. Calculate the midpoint Riemann sum for n=4, being sure to show all work. Use a calculator to calculate the left Riemann sum for n=64. f(x)= 1-x^2 on [0,2] ; n=4 (b) For the previous function on the given interval, calculate the definite integral using the infinite limit of the Right Riemann Sum.Riemann sums from tables Estimate the area A under the graph of ƒ onthe interval [0, 2] using left and right Riemann sums with n = 4, where ƒ is continuous but known only at the points in Table shownMax sine sequence Let an = max {sin 1, sin 2, . . ., sin n}, forn = 1, 2, 3, . . ., where max {. . .} denotes the maximum elementof the set. Does 5an6 converge? If so, make a conjectureabout the limit.
- Minimum sum Find positive numbers x and y satisfying the equa-tion xy = 12 such that the sum 2x + y is as small as possible.number 98 in strang and herman calculus 1. Can you provide a full work up as well as an explanation of the steps? I am struggling with finding 0/0 using direct substitution. https://openstax.org/books/calculus-volume-1@24.1/pages/2-3-the-limit-laws 98. limh→01a+h−1ah,limh→01a+h−1ah, where a is a non-zero real-valued constantThe function f satisfies f(0) = 20. The first derivative of f satisfies the inequality 0 ≤ f'(x) ≤ 7 for all x in the closed interval [0, 6]. Selected values of f' are shown in the table above. The function f has a continuous second derivative for all real numbers. (a) Use a midpoint Riemann sum with three subintervals of equal length indicated by the data in the table to approximate the value of f (6). (b) Determine whether the actual value of f (6) could be 70. Explain your reasoning. (c) Evaluate (integral sign (4 on top/ 2 on the bottom)) f''(x)dx. (d) Find lim (x (goes to 0) ) ((f(x)) -(20e^x))/(0.5f(x)-(10))
- The function f satisfies f(0) = 20. The first derivative of f satisfies the inequality 0 ≤ f'(x) ≤ 7 for all x in the closed interval [0, 6]. Selected values of f' are shown in the table above. The function f has a continuous second derivative for all real numbers. (a) Use a midpoint Riemann sum with three subintervals of equal length indicated by the data in the table to approximate the value of f (6). (b) Determine whether the actual value of f (6) could be 70. Explain your reasoning. (c) Evaluate (integral sign (4 on top/ 2 on the bottom)) f''(x)dx. (d) Find lim (x (goes to 0) ) ((f(x)) -(20e^x))/(0.5f(x)-(10)) I don't quite understand and only need help on part d please, the rest I already know, thanks.Summation of n = 0 to infinity of (x3n) / (n!) Find radius and interval of convergence.Riemann sum & excel Approximate the area of the region bounded by the graph of f defined by f(x) = 100 −x^2 and the x-axis on [0, 10] with 20 subintervals, using the midpoint Riemann sum. Use Microsoft Excel to calculate the midpoint Riemann sum. As attached, is that correct? Can I make a riemann sum graph on excel?
- 1) Find the area (in square units) of the region under the graph of the function f on the interval [−11, 9],using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x) = 9 2) Find the area (in square units) of the region under the graph of the function f on the interval [−1, 5]. f(x) = 2x + 4There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than x approaches p(x) ≈ x / lnx . Use this approximation to estimate the rate (in primes per 100 integers) at which the prime numbers occur when (a) x = 1000. (b) x = 1,000,000. (c) x = 1,000,000,000.ApproximateSin(x) [-pie/2, pie/2]by Riemann sums with the partition P = {-pie/2, -pie/6, pie/6, pie/2} , using first the left sum, then the right sum, and finally the midpoint sum. Use pi for pi in your answers when needed.