17 and g(x) = 'Vx, find (f o g)(x) and (g o f)(x). Then determine wh %3D fo g)(x)?

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: Find partial derivative, zg and Zy for the following function: e 2x²+3y Z =

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Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

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Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: Find the general solution to the ODE using the method of Variation of Parameters: y" + y= cos² x

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Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: 3) S x tari'x dx X,

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Q: ential equati x²y dy = C

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Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: 11. Verify that wxy = Wyx for w = e* + x ln y + y ln x

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Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

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Q: The integrating factor of the linear DE of order one + y csc x = sin x is dx

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Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Find the partial derivative dz for the function z = cos(x³ +y²).

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: by using beta function Vxe-x dx

A: We have to evaluate integral value by using beta function.  I have explained in details please check…

Q: determine dy/dx of the implicit function: 2x2y-sinxy2+e-xy=10

A: Given implicit function is  2x2y-sinxy2+e-xy=10 To find: dydx

Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: Find dy/dx by implicity differation.

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Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: The expression Tyi is an integrating factor for x²y³dx +x(1+ y²)dy = 0. 2xy³

A: x2y3dx+x1+y2dy=0                      (1) If 12xy3 is an integrating factor then multiplying it with…

Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

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Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

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Q: x dx using Sim | size 0.3 is

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Q: The Bernoulli's equation dy +ytanx = y'sec x after multiplying dx -2y and use appropriate…

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Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

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Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

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Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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

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Q: 1 B3. Evaluate dx, using substitution method.

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Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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