Q: Use Lagrange's Formula to Prove that :

Q: A- Find all values of z such that sinh(z) = e'ő. B- Are |z], Img(z) analytic? Give reason.

A: Solution of the problem as follows

Q: Use symmetry to evaluate the followingintegrals.

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Q: Show that each function in satisfies a Laplaceequation. ƒ(x, y) = ln√(x2 + y2)

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Q: For the function f(x.y.z) = sin'(5xyz), find fy. fy. and f (Type an exact answer, using radicals as…

A: f(x,y,z) = sin-(5xyz) fx = derivative with respect to x fx = 5yz/1-25x2y2z2 fy = 5xz/1-25x2y2z2 fz =…

Q: Prove that the Lagrange's formula can be put in the fom ø (x) f (x,) n P „(x) = Ë Σ %3| r= 1 (x- x,)…

A: The Lagrange's formula is…

Q: 2 2. L(sin 2x + e2x+3) = s2+4 s-2 Hint: e2x+3 = (e²2x)(e³)

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Q: 4r2-8)3/2 dz

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Q: S Vx dx d.

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Q: b) fex-c - cos x + 1dx

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Q: find the length Of the Curve fram this merval to

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Q: Evaluate using the substitution u = 1 − x2 or trigonometric substitution.

A: Given: ∫x1-x2dx  ……1

Q: ST,¥. xキマ 1. Verify C ノyジ * =ンycO

A: Since, we are asked to solve using Stokes theorem only, we will use theorem to evaluate the integral…

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: Find the tangent of ZD. 3/3 2V10 E Write your answer in simplified, rationalized form. Do not round.…

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Q: find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral…

A: Here, we use the substitution x=(sect)^2, as we know sec^2t=1+tan^2t, so x^2-1=tan^2t

Q: 2. Evaluate J dx x²√√x²-49) x>7, using a trigonometric substitution.

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute  take…

Q: of Use the definiion Çaplace to determine the fessz e

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Q: Use the Intermediate Value Theorem to show that the following equation has at least TWO distinct…

A: From the intermediate value theorem, For a continuous function y = f(x) in the interval [a, b] such…

Q: JxV1+ x² dx 8.

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Q: 2. Vy+1-2 dy

A: ∫vn dv = vn+1n+1+C

Q: By using u = tan 0, evaluate tan 0 sec*e de.

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Q: Eind the first Rour terms non-Zero in the maclauring Seri es for Por sin X

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Q: Find the root of the function ((x) =sin x -e in the interval (0,1) using the formula g(x) =aresin…

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Q: Given the function g(x) = :/ V4 + sin(31) dt, 2x3 use the Fundamental Theorem of Calculus Part 1 to…

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Q: d 1 (cot-'x) : dx Prove that 1+x?"

A: Let y=cot-1x. Then coty=x.

Q: The function f(1)3 sinh(In()) Is equivalent to which of the following functions Select one

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Q: Use the Newton-Raphson method to find a root of the following function. Start from the initial guess…

A: Given f(x)=1x2-cosx-0.5f'(x)=-2x3+12xsinx f(7)=0.4f'(7)=0.0841x1=x0-f(x0)f'(x0)=7-0.40.0841=2.243…

Q: nd the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form…

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Q: use the distance Formula tO Find the distance between e) and(3,2)

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Q: Use the Reduction Formula to evaluate the following (a) f sin“ x dx (b) S tan x sec4 x dx

A: (a) The reduction formula for ∫sinmxdx is given as the following.…

Q: Use the Intermediate Value Theorem to show that the following equation has at least TWOO distinct…

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Q: Use the general form of Parseval's equality to show that i sin w (sin(w +2) dw = 0. w + 2

A: To Show : Use the general form of Parseval's equality to show that  ∫-∞∞sinωωsinω + 2ω + 2dω = 0

Q: Given LM tangent to OC at point L, which is an expression to represent mJK ? K a° M

A: We have the given figure as The inscribed angle theorem states that an angle θ inscribed in a…

Q: Q: Prove the transfurm; formula's by definition of Laplace

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Q: Steve uses the trignnometric substitution tan ()to evaluate / e) de After simplification, the…

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Q: Evaluate the convolution, f(t) * g(t) = e®t * sin (t), then evaluate at t = 1.

A: Solution:

Q: @lProve f A=3i+ rotating an ang

A: we have to prove that the length of the vector 3i+2j+k does not change when rotating the axes around…

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

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: Given that f(x) = x² sinx, use Leibniz's theorem to find Ⓒd ²³ f dx²³

A: Here the given function is f(x)=x4sin(x). We have to find the third order differentiation of f(x) by…

Q: Given f(x) = sin(5x + ) a) Use P3(x) to approximate f () b) Use Lagrange error bound to show S ()-…

A: (a) The Taylor's series of sin(x) is as follows: sin(x)=x-x33!+x55!-x77!+x99!-⋯ So, we get…

Q: The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the…

A: Solve the given problem.

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: Given: TI || HR Prove: AGHR ~AGTI H R

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Q: Use laplace trasfarng fo Solve dt² 2e cosi2t +e Sin at

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Q: -4 sin bt

A: Recall:         The First shifting Theorem:               L eat f(t) =F(s-a) ℒsin(bt)  =bs2+b2

Q: Use the Intermediate value theorem to show that there is at least one real root of the equation cos…

A: Given, cosx=x3

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: b. Determine real (e/z) in terms of x and y. C. Use Euler's formula to prove that expression; = cos…

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Q: (d) Derive the formula cosh-"(x) = ±In (x + vx? – 1). -1).

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