a. Show that If z = x+ iy where y < 0 Then: | ei*|> 1 b. Evaluate: cosh?(-z) – sinh²(z)

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Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

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A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: ди k > 0 at Ans. u = e'(A,eka! cosh ax + Bjekai sinh œx) u = e¯'(A2e' u = e"(Azx + B3) k ¯kai 'cos…

A: The given problem is to find the solution for the given partial differential equation in different…

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A: Solve particular integral in above differential equations.

Q: Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: e+e¯ (a) Find all the solutions of cosh z 4 (Hint: cosh z 2

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Pind the derivativa otthe Pollowing の3=2 Sin'Csx) In coshラX 3 =\nx (3) Xsin 4y=Jtan YX

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Q: In solving the antiderivative of f(x) =- 2- sin(x) by miscellaneous substitution, the substitution…

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Q: a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that…

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Q: Q.3 Evaluate the by using the appropriate u –sustitution. cos (ln x) dx

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Q: 9. Using n= 8 approximate the value of cos(1+Vx )dx using (a) the Midpoint Rule, (b) the Trapezoid…

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Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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

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Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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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: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: 2. Find a closet rank-1 approximation in the f norm to A = cos 8 - sin e sin e cos 0

A: According to the given information it is required to find closet rank-1 approximation in the l2 norm…

Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: See image below....

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Q: Si (e0.5x +sin2x)dx, use n = 4

A: Solution

Q: 3) by using a

A: sin(12π13)=f(a)+f'(a)*h=cWe need to break it in Taylors series:f(x±h)=f(x)±hf'(x)±h22f''(x)±...

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: ons z = sin y arn

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Q: 1 In AABC, AB = xcm, BC=(4- x)cm, ZBAC=y and ZBCA = 30°. Given that siny show that =D4(v2-1) (5…

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Q: Sind for fca)= Sど+る)(コxー4) by Loyari thim differendional. use

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Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: Verify the rule by differentiating ∫ du/(a2 + u2) = (1/a) arctan (u/a) + C . Let a &gt; 0.

A: Consider the given integral identity. ∫dua2+u2=1aarctanua+C Differentiate the LHS of the equation…

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: dy If y-3z sinh p z cosh y is exact, then n

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