- Question 5 5 Consider f(I) = 2+ 22 1 point For this question, we want to estimate the area under the curve between c = 3 and x = 5 using a Riemann Sum with left endpoints and four rectangles of equal width. How Did I Do? (a) List the four endpoints (in ascending order) that will be used in the sum with left endpoints. CO= 90 1 = In = (b) Find the value of f at these points. Give your answers with an accuracy of three decimal places. f(*0 ) f(z ) = Number f(I, ) = Number f(x3) = Number (c) Find the value of the Riemann sum with left endpoints and four intervals of equal length for f between = = 3 and x = 5. Give your answer with an accuracy of three decimal places. LA = Number- Question 6 The following limit represents the definite integral f(z) da for some real numbers a and 6, and an 1 point integrable function f: n 2z How Did I Do? lim 2+ n-00 n2 n a) Find Ax and a; from this expression and deduce the values of a and b, and the function f. FORMATTING: Your expression for Ax should be an expression involving n. Your expression for ; should be an expression involving the index i and n. The numbers a and b are real numbers, and f(x) should be a function of x. Write your answer in the form [Ac, I; , a, b, f(x)] including the square brackets [ ] and commas (,) between each term. Strict scientific calculator notation is required in your answer, meaning in particular * for multiplication, e.g. 2x must be written 2*x, and (x + 1) (x + 2) must be written (x+1)*(x+2). Answer: [Ax, X; , a, b, f(x)] = b) Compute the value of the limit above. Give your answer with an accuracy of four decimal places. n 2z Answer: lim Number i= n2 nQuestion 9 1 point How Did I Do? We want to use a Riemann sum with right endpoints to approximate the value of the denite integral 4 am f a sin ( ) 11$ 2 5 a} If you divide the interval [2, 4] into 6 subintervals of equal length, you get 6 intervals of the form [11:13 (Ill-+1] whose union is the interval [2, 4]. List the endpoints of these intervals from left to right. Don't forget the square brackets and list the elements separated by commas. Answer: [m,zl,...,$6]: E] b} Compute the value it of each term of the Riemann sum with right endpoints and list your results from the interval the most to the left to the interval the most to the right. Write your answers with an accuracy of two decimal places. Don't forget the square brackets and list the elements separated by commas. Answer: [t1,t2,. . . ,t5] = E] c} Compute the value of the Riemann sum with right endpoints. Write your answer with an accuracy of two decimal places. Answer: N umber - Question 11 6 First let h(u) = cos(x) dx. 1 point How Did I Do? dh Then du 6 Now let g (t) = 4t cos (@) de . Then dg = dt