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Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: A force of F (x) = x² – cos (5x) + 3 where X is in meters, acts on an object. How much work (in J)…

A: Topic: application of integration

Q: (e) Inside r 3 sin 0 and outside r = 1+ sin 0

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Q: aw 1(dw If w = f (x,y) and x=r.cos0, y=r.sine Prove that - * = $² + fy² ar 2a0

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Q: а L {sinh(at)} : given that sinh (at) = So %3D s2 -a? 2

A: This is a problem of Laplace transform.

Q: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

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Q: Show that if z = x+ iy, then: | cosh-z|2 sinh x Hint: use the equation: | coshzf = sinhx+ cos"y

A: We have , z = x + iy We know that ,  coshz = ez + e-z2 Therefore , cosh (-z) = e-z + e-(-z)2 = ez +…

Q: Q.5/ Show that sin(z) = sin(x) cosh(y) + i cos(x) sinh(y)

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Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

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Q: du du 1 If u = tan show that r + J: sin 2u. %3! ar X-y

A: To show the given expression using u.

Q: QuestionTO cos( z+ Da sin(e-2+ In(z)) + C 4 Ob. -4 sin(e-z+ In(z)) + C Oc. --- sin(e-z+ In(z)) + C 4…

A: Given query is to evaluate the integral.

Q: Find the Re(z) and Im(z) z=sin(e^i3)+sinh(5∠30)

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Q: cosh? z + sinh2z=1 true False O оо

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Q: Hiw/ If isinh Z= siniz, proveThat: sinhz= sinhxcosy +ising cosh x

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Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

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Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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Q: cos='A F'A where A =atib

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Q: B) If sinh e V3 Find cosh 0, tanh 0, coth 0.

A: The function sinh(θ) is called the hyperbolic sine function. It is defined as sinh(θ)=eθ-e-θ2.…

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: e sin z -I lim z+0 16 cos z – 16 (Us

A: From the given problem: limx→0exsinx-x16cosx-16 Now solve:…

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: 21. sin® z dz

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Q: W (sinh x , cosh x) = ? Select the correct response: O -2 -1 O 1

A: We will find the solution using the given operator.

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

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

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

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

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Q: Show that z- sinh z Rcs :* sinh z

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Q: Find y' for y=3 sin?x+3 cosx. A O .BO 5 .CO sinx .D O cos x

A: using formula for first derivative of trignometric function

Q: X sin²= cos7 zcos'dx ·COS 2

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Q: Let y = cosh(ina²) then find y'. Oa. sinh (2a.tra) -1 Ob. O b. O c. - sính(Inz²). 2 O d. - sónh(2a.…

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Q: Evaluate: sin z dz +(°z – z)

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Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

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

Q: a z given that z С. Show that sin-1У ôxôy ôyôx

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Q: Sinx n to 5. Airod ht Let fix)=) Find fio) ) and f"to)

A: According to question given thatf(x)={sinxx,x≠01    ,x=0

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: aw C. If w=f(x,y) and x=1. cose, y=1. sine. Prove that aw +1 (0)² = x² + ²

A: Using chain rule

Q: When using u substation what should I use as the u when the problem is the intergral of…

A: Explanation:The given integral is ∫cos3(θ)sin(θ)dθ.

Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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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: If g(z) = cosh a, then g' (x) = _? . O 2 cosh a sinh 2 O 2r sinh a O 2 cosh z O 2r cosh 2

A: Given : g(x) = coshx²

Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

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

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Q: 13) sin z cos r dr

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

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

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Q: Question attached as photo

A: To verify the values of the given definite integrals

Q: y = In(x) In(x)sin(In x) In(x)cos( Inx) y(x) - cjcos(In x) + cysin(In x) cos(In(x)) + sin (In x) x>0…

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Q: Mclopens serial f(x) = cos x she ?

A: Given function is f(x)=cosx