Suppose that f(0.25) = f(0.75) = ß. If the Composite Trapezoidal rule with n = 2 gives the value 4 for f f(x)dx, and gives the value 3 with n = 4, then B=: Select one: о а. 1 b. 2 С. 3 d. 4

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

A:

Q: For a given table 6. 10 14 y 4 12 Find the value of at x = 2 using forward difference formula. dy dx…

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 4 10 In(x) dx, n = 6

A:

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

A:

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: For the position function ​s(t)=−16t^2+108t​, complete the table shown below with the appropriate…

A:

Q: Find the amount of medicine to which the body is most sensitive by finding the value of M that…

A: Given

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: Suppose that a particle moving along the x-axis encounters a resisting force that results in an…

A: Definition used -                   v=∫adts=∫vdt

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

A:

Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

A:

Q: Find the value of dy/dx at the point (-2, 1) for the function which is defined implicitly by x²y – -…

A: Differentiate wrt x

Q: If y = t“, then dy 4t³. dt

A:

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

A:

Q: Suppose the fanction -2t f(t)=te Vepreseuts the Velacity cmeasured in meter/second) of an object at…

A:

Q: Obtain dy from the following function y=e'

A:

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: . On what interval is the curve y = . dt +t+ 2 concave downward?

A: For y to be concave downward, it's second derivative y''  < 0 We will use the Leibniz rule to…

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

A:

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

A:

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

A:

Q: find the values of the derivatives dw/dz at z=4  if w=z+sqrt(z)

A: Write w using an exponent Then use the power rule to find the derivative of w with respect to z.

Q: For the position function s(t) = - 16t + 104t, complete the table shown below with the appropriate…

A: In this question we have to find the Average velocity for each interval given in the table. We can…

Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: To find the size of order that will produce a minimum cost, begin by finding the derivative of…

A: To find the value of x at which C has minimum value. C=3x+600,000x

Q: For the position function s(t) = - 16t + 104t, complete the table shown below with the appropriate…

A: The position function is given as st=-16t2+104t We know that , The average velocity formula over the…

Q: Two ships are sailing in the fog and being tracked on a small screen. At some point in time, t=0,…

A: Hi, thank you for the question. Since you have posted a question with multiple sub parts, as per the…

Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

A:

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

A:

Q: (b) How many subintervals ( find the smallest n) needed to approximate dxusing the Trapezoidal Rule…

A: Step:-1 Part (a) Lagrange Interpolation Polynomial of order 2:-   f(x)≈fx0 +x-x0fx0-fx1x0-x1…

Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

A:

Q: A whole life policy is issued to (30) with Z=10 for T20. If the force of interest and mortality is…

A: We have to find actuarial present value of the benefit for this policy

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: If f(x) • g(x) is to be integrated with respect to x, taking dx as the differentiated variable,…

A:

Q: 4 S X the condition that the error for Trapezoidal Rule will be at most 10-6. 9. Given: dx.…

A: The error bound for the Trapezoidal rule is given by the formula E≤b-a312n2maxf''x where a is the…

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x3+y4=3

A:

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: the position function of a particle is given by s (t)= 3t2-t3, t greater than or equal to 0. a.…

A: The position function of a particle is s(t)=3t2-t3, t≥0

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

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.