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

Q: Suppose that the error for the composite trapezoidal rule is given by h2 f" (µ), µ E (a, b).…

A:

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: 1. What is the length of segment XY?

A: Given,

Q: Use the error bound for the trapezoidal rule to find the smallest N such that the error in…

A:

Q: show that the square of the length of subtangent at any point on the curve by2=(x+a)3(b is not equal…

A:

Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

A:

Q: Define the moment-ratios ß1 and B2.

A: To define the moment-ratios.

Q: Use the Trapezoidal Rule with n=6 to approximate π∫0sin2xdx.

A:

Q: the segment XY

A: What is the length of the segment XY

Q: Find the midpoint OF the line seament given the FOllowing endpaints:(s,2)and(-u,1)

A:

Q: The gruph o i shown here Ideatify the graph of the inerve finction - (B,

A: The inverse of a one-to-one function f(x) is another function that reverse the function f(x). That…

Q: The perimeter of a circumscribed polygon was used to find an approximation for pi by the ancient…

A:

Q: Show that T,+M, = S2n- Mn=S2n-

A: The given relation is  13Tn+23Mn=S2n Here, Tn is a trapezoidal approximation, Mn is the midpoint…

Q: Q2: A-The Trapezoidal rule for roodx 5 and Midpoint rule /)dx=4 What value does . Simpsons rule give…

A: 1st we will find relation between trapizoidal , mid point and simpson rule . Then will use this…

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: use Lagrarge mul tipliers Sublect to the Constcair t to mekim,ze x+2y=5

A: Consider the given information. fx,y=x+4xy+6y and x+2y=5 Now, make the auxiliary function.…

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y

A:

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 4…

A: Given that  The figure is

Q: @ Consider the task of approximating 3x2 using the Compoute trapezoidal rule. How large should n and…

A: The error term in the composite trapezoidal rule is  h212b-af''ξ , where h=b-an Given f(x)=e-3x2…

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

A:

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Use Simpson’s Rule with n  =6  to estimate the length of the curve x  =t - et -6<t<6

A:

Q: Apply the midpoint and trapezoid rules to the following intergal. Make a table showing the…

A: Consider the provided question,

Q: Find the mZR in trapezoid QRST where QT||RS below.

A:

Q: What is the radius of X x² + y² – 6x = -4y + 68? Show all work for full credit.

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Q: Use the composite trapezoidal rule to compute Jo e dx correct to 3 significant gures, taking 5…

A:

Q: Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 %3D and…

A:

Q: Does the followlng intergral Co verge or diverge ? dx

A: Check whether the given integral is and divergence or convergence

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

A: Given query is to find the position of P to maximize the angle theta.

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: is Simpson Rule method or Trapezoidal Rule method is accuracy: 1- L1-e dx, , 8 = 10-9, N = 12 %3D

A: Use the following formulae, to evaluate the definite integral. Trapezoidal Rule:…

Q: From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is drawn perpendicular to the…

A:

Q: 9-The uolome of Abe colar height y is hy VE xy. Soppose that the uolome a right cir cular cone af…

A: Given a right circular cone with radius x and height y. Then volume of the right circular cone…

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: A randon veniable is uaiform ly distabutzd over whit is its skew ? t's

A: The pdf of uniform distribution is as follows:

Q: 5. Given: C is the midpoint between C Prove: B E I

A:

Q: B- Use the Trapezoidal rule with n=2 to estimate dx, to find the absolute relative true error |E,?

A:

Q: Find the length of the curve x = y²³² +1 on 21 44 чу 3≤7≤5. □ стуре fraction, or round to the an…

A: To find the length of the curve.

Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

A:

Q: Determine whether each of the following statements is true or false, and explain why Simpson’s rule…

A: Given statement is  Simpson’s rule usually gives a better approximation than the trapezoidal rule.

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Kis the midpoint of segment L. JK = 6x and KL = 3x +3. What is the length %3D of JL? * 12 18 36

A:

Q: In the diagram below, XY is tangent to OCat point P. What is m2CPX? Explain.

A:

Q: Two tangents are drawn to circle O from external point P. If the major are formed has a measure of…

A: Let m∠P=x°

Q: Given: APQR has a right 2Q. M is the midpoint of PR. Prove: MP = MQ = MR

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.