) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = cos x −…

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Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

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Q: Do the functions y, = cos4t and y, = sin4t constitute a fundamer %3D The functions constitute a…

A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: 2.3 Find the general solution of p fanx+q tany =lanz

A: Given:   P tanx+q tan y=tanz→           1   is of the form pP+qQ=z:

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: 4) Verify the identity using the definitions of hyperbolic functions. e2x + 1 e2x – 1 coth x

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Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

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Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 42 x3 –…

A: Implicit differentiation

Q: Find exact Values for x in the interval 0,36O°) that satisfY the equation. 3Sin 2x+25inx=1+3cosx

A: We know that the formula of sin(2x) = 2 sin(x)cos(x).

Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: 6) Find (cor dy of

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: The base of a three-dimensional figure is bound by the graph x = cos(y) + 1 on the interval [-n, r].…

A: Option(2) is correct answer.

Q: Evaluate. d farctan a – In a] dæ 1+x² 1 sec2 x 1 :- e" sec² ¤ 1 + 1-x²

A: The rule of derivatives states that ddx(f(x)±g(x))=ddx(f(x))±ddx(g(x))

Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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Q: The Wronskian, W, of the functions y1 = sin(2x) and y2 cos(2x) is %3D

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Q: Sketch the periodic extension of the indicated function.

A: According to the given information, it is required to sketch the period extension of the indicated…

Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: See image below....

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: Show that U(,y) is Harmonic function and find its conjugate for U(x, y) = 2x – x³ + 3xy² -

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Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: Fand ar a of functrons COSX n

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Q: In Exercises 1–18, find dy/dx. cos x 1 + sin x 12. y = cos x 14. у — cos x

A: As per Bartleby's guidelines. we are allowed to solve only 1 question at a time. Apologies for the…

Q: Use the Intermediate Value Theorem to show that the equation  t^2 - cos(t) = 0  has at least one…

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Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: Find the points of inflection and discuss the concavity of f(x) = 2 cos (3x/2) on (0,2pi)

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Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

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Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: 4. Use the first Fundamental Theorem of Calculus to find 3r 2-1 dt 12 +1 sin 2z

A: Fundamental theorem of calculus Let us consider the continuous function f(x)  on the interval [a,b]…

Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

A: Given equation is f(x)=x2-4sin(x) Initial approximation is x0=3 Now f'(x)=2x-4cos(x) formula for…

Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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