Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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A: Cauchy residue theorem is used to find the integral of a closed curve. Cauchy residue theorem says…

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A: Given expressionConsider  Taking natural log both sidesOn substituting the limit x =0 it makes…

Q: 5. Prove that (Z, × Z6)/((2,3)) S Z12.

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

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Q: 2. A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

A: A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

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A: Given function is Now differentiating it twice we get  Noted that there is no x for which  , In…

Q: 12 +3t-4 and 3t2-3 9.) Suppose that x = 3x 10

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Arg (zz) = 0, whenever :+ 0

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Q: (x° – xº) (1+x³)5 Evaluate dr; Use B(m, n) = dr (1+x)m+n

A: Using the given result and

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Q: 5. Find Wxxyyz, Wzyx, and მაw Əzəx²ǝy² if w(x, y, z) = x³y-5 + sin(xyz) + In(x + yz). C

A: Note: All partial derivatives are not small. I can solve only first two partial derivatives as no…

Q: 10.) cos*x

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Q: 6. f cos³x√sin xdx)

A: sin2x+cos2x=1∫xndx=xn+1n+1

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Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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Q: FOR THE FUcnoH Xe*, FIHN THE MACLAURI SEAIES APPROXIMA TIOU

A: Given:

Q: (15.2): Find In(x) – In(x² – 1) +2 In(z +3) 3

A: Find 13ln(x)-lnx2-1+2lnx+3. Logarithmic properties used: alogcb=logcba logca-logcb=logcab…

Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

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Q: 2 Evaluate: ²₁²(x²-y²² du dt

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Q: ( 82) Ex: Find the Faurier exfansionof fex+

A: The Fourier series of given function is given as follows :

Q: If A(x)= 5x (1) - AP() = 1 1 + f² dt then:

A: Ax=∫05x11+t2dt

Q: sin-¹ x = sin , prove z +Zxx = 0.

A: Given x = sin-1(z/y)  We have to prove,  z + zxx = 0