dy Find the value of at x= 5 using Lagrange's interpolation formula from the given table dx 1 7 y 4

Q: For a given table 10 14 y 4. 12 20 dy at r = 2 using forward difference formula. dx Find the value…

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Q: If x = t-t3 and y = t2-t, the value of at t 2 is dx 11/28 The answer is not mentioned 2.5454

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Q: Given that y = ln a-7, find d %3D O dx dy d.x ||

A: GIVEN : y = ln |x2 - 7|

Q: Ca) Supposed that w= xy – x2 with x = e¯"s²t and y = r²s sin t. Find the value of when r = 0, s =…

A: Given:  w=x3y-x2     , x=e-rs2t      and y=r2s sintsubstituting x=e-rs2t      and y=r2s sint in…

Q: Evaluate dz using the given information. z = 5x3 + 2xy2 - 4y; x = 1, y = 3, dx = 0.01, dy = 0.02

A: Evaluate dz using the given information. z = 5x3 + 2xy2 - 4y; x = 1, y = 3, dx = 0.01, dy = 0.02…

Q: If z = x² – xy + 7y2 and (x, y) changes from (1, –1) to (1.04, –1.05), compare the values of Az and…

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Q: dy d'y Find dx' dx² formula, from the given data: at x= p, p+0.5, Using Newton's forward…

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Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: 2.8 S = | f(x)dx =?

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Q: 2: For a given table 2 5 8 11 y 4 8 13 18 (c) Using Lagrange's interpolation formula, find the value…

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Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: Use the formula for the slope of the tangent line to find 2 of c(t) = (5t + 9, 3t – 8) at the point…

A: The curve is defined by the following parametric equation  c(t) = 5t+9,3t-8 Where, x = 5t+9 and y =…

Q: Find dx by differentiating implicitly. When applicable, express the result in terms of x and y. 7x…

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Q: 2. Let y = x? 4x2 . LA. Find "dy". B. Find the value of "dy" when x = 4 and dæ = 0.01.

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Q: 4 dx 1+ By using (Answer one only) a- Trapezoidal rule when n=5 b- Simpson's rule when n=6

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Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: Låt f(r, y) = 1+ y? Given the absolute errors Ex in x and Ey in y, derive a formula for the absolute…

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Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x&gt;0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: Find ds/dx if= y= In[(2x^3+7) (9x-2x^2)]^5 Hint: Use the Tattoo and the Properties of Logs

A: Given y=ln2x3+79x-2x25 Using properties of ln, 1) ln an=n·ln a 2) lna·b=ln a+ln b  y=5…

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

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Q: dy Find the value of dx z for the following In x b. x³ + y? + 4x²y – 25 = 0 3 a. Y = (sin x) || %3D

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Q: For the given DE with coefficients linear in two variables, do the following: (6x – 3y + 2)dx – (2x…

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Q: So (xs +x) dx 24.47 %3D The bet ween y = sin x and the x - axis for area

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Q: For y=f(x)=3x^3 , x=3 , and (triangle)x = 0.03 find dy (two decimal places)

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Q: ôf Find dx fe for the following dy and x?y (a) ƒ(x,y) = y4 + 3

A: Consider the given function: fx,y=x2yy4+3 Here, the objective is to find the value of ∂f∂x and ∂f∂y

Q: dz (a) Find of the following functions: dx zx2+1cos y? = sin(y? + 22z)

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Q: dz = 2ni to deduce that z+1 Use the fact that (x+1)dx+ydy Sc O (x+1)dy-ydx = 0 and Jc (x+1)²+y² =…

A: Given ∫c1z+1dz=2πi ......(1)we have to prove that ∫c(x+1)dx+ydy(x+1)2+y2=0 and…

Q: H.W: Given that approximate 1 dx=2 use Trapezoidal rule with n=8 to 9 x² +1 4 the value of ß?

A: Trapezoidal rule

Q: Given that x = e'Iny, y > 0 dx (a) Using the product rule find an expression for dy dy and hence…

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Q: (x³y³ + 1)dx + x*y?dy = 0

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Q: Given that 7 < f(x) < 8 for 1 < x < 2, | f(x)dx estimate the value of / s(x)dx < VI

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Q: Given: f(x,y) = x³y – y cosh x" Solve for D132

A: Given:                   fx,y=x3y-coshxy To find: The value of the partial derivative D132.

Q: dy Find for the following function dv y = In cosh v – tanh? v

A: We have to find dy/dv by using derivative of hyperbolic functions.

Q: Lind -2x+H where X- oro Zy

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Q: Use integration by part to obtain a formula for S x"e*dx and use it to find S x'e*dx. Bx

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Q: for f(x, y) = cot(x² + y²) dydx 4. Find

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Q: If z = 9x + y² and (x, y) changes from (1, 3) to (0.95, 3.1), compare the values of Az and dz.…

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Q: 4 | f(z)dx 14 what is 3 | f(2)dz? Given that 4 answer

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Q: Given the IVP dy + 4y = x - 2, y(1) = 0, dx the value of y(2) is closest to

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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Q: owing ODE is exact and solve for x(t). dx - - xtan(x) + sec(t) =0 x( dt Where a = (1+Q) with Q being…

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Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Given that: 0 V40x – x² dx Find the value of m

A: From the given problem: I=∫04040x-x2dx So, we can also write as: ∫04040x-x2dx=∫040-x-202+400dx...1…

Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

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Q: Given y = V1+x³, find dy/dx. Use this result to find the approximate change in the value of y when x…

A: As we know that the instantaneous rate of change at any point x = a is approximately equal to the…