24.) Given the function f(x)=x²– 2x Estimate J f(x) dx using four subintervals by . finding R4, L4 and M4.

Q: (b) Solve for the optimum to the following problem using the Karush-Kuhn Tucker conditions: Optimise…

A: Solve the following using the Karush-Kuhn Tucker conditions: Optimise fx1,x2=x1x2s.t.…

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: 10- Compute the following estimate of J f(x) dx using 8- the graph in the figure. M(4) 6- 4- 2- 0-…

A: Hair we have to use the midpoint rule

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: 6. For the function f(x,y) = 8x³ – 12xy + y3 a) Find all critical points of f (x, y)

A: Solve all the three parts for the given function f(x, y)

Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x - 3x2 + 2). dx

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Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

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Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f(t) to y′ = t -…

A: Given, y'=t-2y y(2)=3

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Find the general antiderivative of f(x) = 4x – 5. Use Cfor the arbitrary constant. nswer F(x) =

A: Fx=∫fxdx

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: f(x)=x²-2x Sf(x)dx using four subintervals by on Estimate -1 d M4.

A: Given function is We divide the interval [-1,1] into four sub-intervals with length of each is…

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: For f(x, y) = 2y3 + x² – 4x – 4xy – 9, find the critical points and use the - Second derivative test…

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Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: -10 Estimate J f(x) dx using five subintervals with Right endpoints b. Left endpoints Midpoints а.…

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Q: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: Integrate f(x) = 0.5 + 20x + 3x4 from a=0 to b=3, given N=12 by using a) Simpson's 3/8 approximation

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Q: Find the root of f(x)=(x-4){(x+2)= 0, using the initial guesses of x, =-2.5 and Xy = -1.0, and a…

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Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: Suppose that a function f(x) takes the following values: 1 3 f(x) 2.4 2.0 3.5 5 Calculate the…

A: The Trapezoidal Rule formula with n=2 subintervals is written as T2=∆x2fx0+2fx1+fx2 where…

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

A: We apply Simpson 1/3rd rule it is given that six sub intervals must be mentioned so in the interval…

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

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Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

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Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

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Q: 2. Use the secant method to estimate the root of f(x) = a° + a³ + 3. %3D By starting with the…

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Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

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Q: 4.1 Use the trapezoidal rule to find an approximate value for V1+x'dx with n = 4.

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Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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Q: By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the…

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

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