In Exercises 71, and 72, fill in the blanks. (Note: The notation x → c* indicates that x approaches c from the right and x → c¯ indicates that x approaches c from the left.) As x→n+, sin x→ and csc x →

Q: e*, when 20 = -1 %3D P„(x) sin(nrx) – nn cos(nax), when 2, = (nx)² for n = 1,2,3,.... a.) Show that…

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Q: In Exercises 1-8, find dy/dx. 1. x²y + xy? = 6 2. x + y' = 18xy %3D 3. y2 =-1 x+ 1 5. x = tan y e X-…

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Q: In Exercises 21–26, find the discriminant of the given function. 21. f(x, y) = e2* cos y 22. g(x, y)…

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

Q: At what points are the functions in Exercises 13-30 continuous? 1 1 + 4 (x + 2)2 13. у 3x 14. y %3D…

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Q: Find y if: (a) y = (In x)cOs z (b) y = In(x² + y²> %3D

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Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: Prove that eax (a cos bx +b sin bx) + C. ax cos bxdx %3D a2 + b2

A: ∫eaxcosbxdx=eaxacosbx+bsinbxa2+b2+C

Q: Exercise 2) Find D constant in the following O(0) function O= D Sin? 0.

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Q: 1. Use the Fundamental Theorem of Calculus Part II to evaluate each of the following: 1 3 a) + 8*…

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Q: Let x (t) =y(t) +sin(t), x2(t)=y (t) then x2(t)= x,(t)- cos(t) Select one: O True False

A: given x1(t)=y(t)+sin(t) , x2(t)=y'(t)

Q: 3. Use the theorem in Sec. 48 to show that (z – zo)"- dz = 0 (n = ±1, ±2, ...) when Co is any closed…

A: The given question is solved below.

Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: 4) For A= a,āx + azay + a3az, B = b,ax + bzay + b3az, show that %3D %3D A.B cos 0 = A.AVB.B

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Q: In Exercises 23–25, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = x - 2y2 + z2 24. ƒ(x, y, z) = (x2 + y2…

A: Since you have posted multiple questions, as per our policy we will answer first question. Given,

Q: In Exercises 23–30, find Tn centered at x = a for all n. 26. f (x) = e", a =-2

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Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: Differentiate with respect to x: y= In(3x2)/x3  and y=x2sinx/cos2x

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Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: u" (x) = -u(x), 0 < x < T, и(0) — и(т) — 0.

A: Step:-1 Given differential equation of second order is  u''(x)=-u(x), ----(1), with u0=uπ=0 and…

Q: Write the DE, e" y' + e2y= sin a in the general form.

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Q: Exercise III (a) Let I = psin(ø) cos (0); y = p sin(6) sin(0); pcos(6). Then find the following. (i)…

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Q: Graph the following vector fields

A: (a)known fact:

Q: In Exercises 7–14, express in the form y = f(x) by eliminating the parameter. 14. x = cos t, y=csct…

A: Given: x=cost, y=csctcott We have to express the given function in the form y=fx by eliminating the…

Q: Exercises 1) Find if z = 3 cos x – sin(xy),x = ,y = 3t -

A: The given equation is; z = 3 cosx - sin(xy) , x=1/t , y=3t

Q: Exercise 15. Let f(z) cos z (z2-1)2 The residue off(z) at zo = 1 is a) – sin 1 b) sin1cos 1 c) -(sin…

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Q: Prove that TIN) F(a – p) O< Re

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Q: Show that cos A x e 2 *,x2 0. %3D

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Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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Q: Exercise 4. * Let f(z) = sin(3z) and C: |z| = 1. Then fe f(z)dz = a. 0 b. 3ni c. -6ni d. None of the…

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: In Exercises 1 and 2, write a in the form a = a tT + a nN without finding T and N. 1. r(t) = (a cos…

A: Consider the position vector

Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

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Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: The values of C, and C, so that y(x) = C, sin (2x) + C2 cos (2x) satisfies the following conditions:…

A: Solution:

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: 59. Prove the general formula 1 I x – a)(x – b) where a, b are constants such that a # b. dx In х —…

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Q: Use the indicated substitution to evaluate the integral. 2x cos(x) dx , u = x' sin (x²) + C 2 sin…

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Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: Let z = x? – x*y where x =r sin 0 and y = r cos 0. əz əz Use the chain rule to find and ar - Give…

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Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

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Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: Let A E R²x2 be special orthogonal. Show that there exists & E [0,27t) such that COS O - sin o A =…

A: According to question,Given Matrix,A = cos ϑ-sin ϑsin ϑcos ϑ

Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

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Q: In Exercises 1 and 2, write a in the form a = aTT + aNN without finding T and N.1. r(t) = (a cos t)i…

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Q: . Let z = x2 – x*y where x = r sin 0 and y = r cos 0. az and ae az Use the chain rule to find ar…

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