Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

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A: Integrating by parts.

Q: is intea rable Primitive aR 2 > X 3 1 2. 1 ラメラ 。 (今さ うx 31 ラ× %3D >入う。

A: we have Fx=0            0≤x<12x-1    1≤x≤2and fx=1     0≤x≤12    1≤x≤2 i The primitive of a…

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A: Solution

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A:

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A:

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A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

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Q: 4.3 Use the calculus of residues to evaluate the following integral (x2- dr. + 1)2

A:

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A:

Q: In(x) -dr

A:

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A:

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A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

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A: Use polar coordinates for simplification of the given integral.

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A: Given that f(x) = 1 + x sin 1x6,x≠00,x=0 To prove that, f(x) is integrable on [0, 1]

Q: F[x₁,...,n] is an integral domain.

A: Solution:-

Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

A:

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: Define Riemann integral in R^3

A: Partitions of an interval-   The partition of an interval [a, b] is a finite set P of points…

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: Evaluate using cauchy's Residue Evaliate theorem.

A:

Q: nsist only of of even length. Generalize to find the EGF number of ations that consist only of…

A: To find: (1) The EGF for the number of permutations that consist only of cycles of even length.…

Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

A: I am attaching image so that you understand each and every step.

Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

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Q: Evaluate Integral. integral 0 to 2 (4/5t^3-3/4t^2+2/5t)dt

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Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

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A: We use integration by parts

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A: In this question we have to evaluate the Integral.

Q: 26) ) Show that the reductión formula for 1ー2 Sec" ndx = Sec atan n t n-2 n-- n-1 ) Hence use tta…

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Q: 2. Use the Intermediate Value Theorem to show that 2.x 3 - if – 3 0 has a zero on the interval [-2,…

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Q: Evaluate the indefinite integral. (7z + 7 71 + -dr Jz² +1

A: Given,          ∫7x+7x2+1dx

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Q: Evaluate the integral.

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Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

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A:

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A: Given that ∫-∞∞x+3 sinxx2+1x2+42dx Using Cauchy residue theorem, we can written it as ∫-∞∞z+3…

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

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Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

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A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

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Q: Prove that 1- cosh-x= In(x+ V?-1 x= In(x+Vx² -1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: by thể differen ntial equation on associated with this sy

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: Prove this equa tion analy tic fcz)z Ln /21+iargz Ln 12|+iarg

A: Equation proving in analytical way

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A:

Q: @ Hiw/ prove that cosiz=coshz @ Cosh'z @ 1- Tanhz - Sechz

A: As per Bartleby's expert answering policy, we can answer only one question with a maximum of three…