Selected values of /(a) are shown in the table below. What is the left Riemann sum approximation for I (#) da using 4 subintervals as indicated by the table? 4. 10 11 2 21 23 26
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- On a sketch of y=ex represent the left Riemann sum with n=2 approximatingUse the Maclaurin series representation of sinh(x) from the table to create a Maclaurin series of sinh(x^2). Next, differentiate it to create a Maclaurin series for 2xcosh(x^2): Find the Riemann sum of f(x) = 3x2 over the interval [-1,1] obtained by dividing the interval into n equal subintervals and using the right-hand endpoint for each ck. Leave your answer in the Sigma summation form.
- What is the Laurent series expansion of an analytic function and how is it used to study singularities?Evaluate the Riemann sum forf(x) = x^2 − x where 0 ≤ x ≤ 2 with four subintervals, taking the sample points to be right endpoints. Explain,with the aid of a diagram, what the Riemann sum represents.A heavy rope, 40 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.)How much work W is done in pulling half the rope to the top of the building?Show how to approximate the required work by a Riemann sum.
- A hotel wants to create a patio that is straight on three sides, but has a decorative curve on the fourth side. A graph of the patio shape is shown in the graph below. Part 1 The contracting company wants to order concrete for the patio, but needs to know the area to be covered. Use a left or right Riemann sum, with an appropriate amount of subdivisions, to estimate the area of the patio.If f(x)= sqrt(x) - 2 and 1 is less than or equal to x which is less than or equal to 6, find the Riemann sum with n=5, taking the sample points to be midpoints. Give your answer correct to six decimal points.