2a. 2b. 2c. For questions 1 and 2, consider the function f(x) =+ x +1 on the interval [0, 4]1210862-3-2-1231) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4] by using n = 4 rectangles andleft-hand endpoints.a)Whats the width, Ax, of each rectangle used in this approximation?人るl4= 2 (6i-)x= f(Xo) + flx) + flx)tfCX3)c0,4) and n=4Given the interval [aib] =b-a4-0= |4こnAxAX = 1b)List the gridpoints, xo, X1, X2, X3, X4, used in this approximation.メi+l=Xit AX'osX, = xo+ AX = 0+1 = 1Xz= 2ド2: Y」t Ax= Itl=2X3 = X2+ AX= 2+1 = 3X3 = 3X4=4X4 - x3+AX= 3+1= 4Gridpoints: 0, 1, 2, 3, 4c)Illustrate this area approximation by sketching the corresponding rectangles in the graph above.Math 1151Written Homework 5Autumn 2020d)Is this area approximation going to be an overestimate or an underestimate. Explain.We hnow that wnen the grapn is con care down Gne second derivative is negative )then me iine Will ve above +hne grapn and theapprox imati on is an overestimare, otherwise it is anunderestimare, cit the graph is con cOne up), From the grapn wecan observe thatthe graph ot fU)< x?+ xtl,on [0,4] wnich is given above as concavevp on c0,41. so the area approximation tor hrs grapn is goins to be anoverestimate .e)Calculate this area approximation.f(XoJ = fca) = fl0)=/+ (K J= fla) = flI)- 914+CXZ) = f(as= PlZ) = 4f(X3) = fla)= P(3)- a5)4ニ 2) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4] by using n rectangles andleft-hand endpoints. (Leave n as a parameter.)a)What is the width, Ax, of each rectangle used in this approximation?Ax =.b)Find a formula for the gridpoint x. (The only variables appearing in your expression should be k and n.)X =c)Write the Riemann sum for this area approximation in Sigma notation.Sigma notation:

a) Given that, the interval is [0, 4] and n=4. It is known that, the formula for ∆x=b-an. Obtain…

2) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4] by using n rectangles and left-hand endpoints. (Leave n as a parameter.) a) What is the width, Ax, of each rectangle used in this approximation? Ax =. b) Find a formula for the gridpoint xg. (The only variables appearing in your expression should be k and n.) Xk = c) Write the Riemann sum for this area approximation in Sigma notation. Sigma notation:

2) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4] by using n rectangles and left-hand endpoints. (Leave n as a parameter.) a) What is the width, Ax, of each rectangle used in this approximation? Ax =. b) Find a formula for the gridpoint xg. (The only variables appearing in your expression should be k and n.) Xk = c) Write the Riemann sum for this area approximation in Sigma notation. Sigma notation:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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