Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: 2) Y is a ramdom variab le which has dety it y o other wise a) Fünd Fy ly)

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Q: 6. Use Green's Theorem to evaluate (y- ry') dr + (2- r) dy where C'is shown below. x +y =

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Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: dy If y = In (x + Vx² + 1) then dx O A. x²+1 O B. 1 Vx? +1 OC. 1 O D. 1 x2 +1

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Q: 1 Evaluate J JA (2²+v²)² dxdy, where A is determined by the conditions 1< x² + y? < 2.

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Evaluate SSS 7e(=²+y²+z?)*² dV over B where B = {(x, Y, z) : x² + y² + z² < 1}. Take T = 3. Turkcen.…

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Q: 3. Let F lt) be the antider¡vatPve of f (t) the most general antiderivative of flt>= 8 sec?(t) -92

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: Find dey -. The initil dx² condition Xo=0i y=10, %%=5&h=,by using yro1), given Runge -Kutta method…

A: Given second order differential equation is d2ydx2=y3                  (1) with initial condition…

Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

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

Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: --- Q#3 Evaluate Cf 2x dV →Where E = {(x, y, z)| 0sys 2,0sx sV 4 - ,0 < z y} ,0 sz< y} Ee

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Q: Which of the following is the antiderivative of S ) dx? xVx+1 Vx+1-1 + C Vx+1- a. In c. In + x…

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Q: If the têst is inconclusive, then say SO. 3* Σ k! k=1 If p = +o, enter "inty". i

A: Given query is to find series converges or diverges.

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: dx = O In|æ| + C O In(x) + C O z° + C O Does not exist.

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Q: 3.Evaluate ex dx, by Simpson's ½ rule. n=6` 1 = (b − a) ƒ (xo) + 4f (x₂) + 6 f(x₂)

A: We have to solve by Composite Trapezoidal Method.

Q: The DE : y = e-/Y is seperable Select one: O True O False on

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: -Skatch the reglén of Etyndtion , reversed the order of itegral and evaluade dx dy 7 | +

A: We have to sketch and after changing the order of integration evaluate it.

Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

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Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: (z In z + 5)dz

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Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

Q: dw If w = x2y sinz - 3zey, find dz 6. O a. dw =x?y cosz - 3exy dz O b. dw =2x2y cosz- exy dz O c. dw…

A: Find the partial derivative of w  with respect to z

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: lx)にX sit. ors<I prove that inl Guernesto uniterady. Guveryes to

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: for 2xey = 4 – In 1024 + 10ln x, with the conditions dt dx = 8, x=2, y= 0. Assume x and y are…

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

Q: 1 +y = zy" dy dr

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Q: L{sin(JF)} = V %3D 4s 2.s2

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Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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