Use the Midpoint Rule with m = n 2 to estimate the value for 5 x + 3ydA on the rectangle R = (0, 8] x [0, 2] !!

Q: Use the Midpoint Rule with  n = 4  to approximate the area of the region bounded by the graph of…

A: Given:    Approximate using mid point rule:∫04x2+4x dx ,  n=4

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

A:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A:

Q: In the given question , use the Midpoint Rule with n = 4 to approximate the area of the region…

A: We have to use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the…

Q: Use the Midpoint Rule with n= 4 to approximate ∫23 (4x + 2) dx. ∆x = ______________ Subintervals =…

A:

Q: Let y Ay - 5x² + 8x + 4. If Ax = 0.4 at x = 5, use linear approximation to estimate Ay I Submit…

A: We know that ∆y=f(x+∆x)-f(x). So,             ∆y=f(x+∆x)-f(x)      =f(5+0.4)-f(5)      =5·…

Q: Use the trapezoidal rule with n = 5to estimate V7 + y³dy

A:

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

A:

Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

A:

Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: find the orthogonal trajection of the family of curves x2+y2=a2

A:

Q: Find two z values so that 53% of the middle area is bounded by them.

A:

Q: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

Q: Let T, be the approximation using n subintervals for the Trapezoidal rule to estimate I = +e*)dr.…

A: Error bounds for the Trapezoidal rule: Let f(x) is continuous function over [a, b], having the…

Q: 10, 6J. the Midpoint Rule with timate the folllowing. IL x. v) da How could you improve your…

A: As m=n=2 Therefore let us take the subintervals as: 0,3 and 3, 6 The midpoints od these subintervals…

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

A:

Q: 22) Find 2 positive numbers xby WHh xY=50 SUch h that 2x+Y is minimized. Round to neakest tenth.

A:

Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

A:

Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

Q: Find the betwween/bounded by area the Curue u=4y-x² and The line. 4=8-Zx.

A: Sketch the two curves From the graph, we observe that both curves intersect at x = 2 and x = 4.

Q: Find the area bounded by the loop of the curve y² = 4x²-x*

A: The given equation of the curve is: This can also be written as: The graph of this curve is:

Q: on of xy-pane for which the eguation would have a n whose graphe passes hroush 2y)in ) dy =ytx…

A:

Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

A:

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

A:

Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: ae e drea under the curvé y=*from2-2to2 using a Rightt Endpoint approximation with 6 subdivisions..

A:

Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

A:

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: Find the area of the region lying to the right of x = y2 - 5 and to theleft of x = 3 - y2.

A: Given: f(y)=y2-5 and g(y)=3-y2 To find: Where the curve intersect and it is calculated when…

Q: 4 to Use the Trapezoidal Rule with n = 1 approximate J-1 V1-x³

A:

Q: Find the local minimum ond local moximunm Cit exists) for the funetion fex,ys = 2x? + y? + 8x -by…

A: We have to find the local maximum and local minimum of the functionf(x,y)=2x2+y2+8x-6x+20 we denote,…

Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

A:

Q: (3) +. R Ris bounded by the semicircle y = V2x – x² and the line y = x

A:

Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

A:

Q: y = Vx - x² - re sen /x

A:

Q: The area bounded by the curve y = 3/x and the lines x = 3 and x = 8 above the x axis - is _square…

A:

Q: 4. Use the bisection method to approximate the root of f(x) = 2x² [0, 1]. Let € = 0.1 be the margin…

A:

Q: 2 : Use Lagrange multipliers method to show that the maximum value of f(x, y, z) = x²y²z² on the…

A: In lagrange method, the Critical points are the points that cancel the first order partial…

Q: Use the bisection method to approximate the root of f(x)=2x²-1 in the interval [0, 1]. Let E= 0.1 be…

A: Bisection method is one method used to find the approximate root of a function within a specified…

Q: (4) Use the Midpoint Rule with n = 4 rectangles to approximate the integral. Round answer to three…

A: The Midpoint rule is

Q: The area under the curve y = 3z bounded by the linesI = 3 and z= 7 above the z- azis is O 174.00…

A:

Q: Find the absolute maxima and minima of the function on the given domain. 6) f(x, y) = 6x + 5y on the…

A: f(x,y) = 6x+5yfx(x,y) = 6     fy(x,y) = 5  (Hence No critical points of the function itself)Lets…

Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…