i? た(uパ) : tan ニ u= X Cosy V= X siny JR Determine Jf to 24 つメ

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: az -? Since it is du coSV.y=. av ) z = In (xry*),x = e"cosv.y= e"sinvr

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Q: The value of 6 dz,where C:|z|= counterclockwise, is sinh(z+2) 7-4 O a. O b. 27isinh(3) sinh(3) O d.…

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Q: 2 cos(2x) dx, n = 4 J1

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Q: O1) Prove that: [Answer only two du dx (A) - tanh u = dx 1-u du (B) u-1 = sec u+C >1 2. (C) cscx =…

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Q: In Exercises 17–20, find dr/d0. 17. r = 4 – 0² sin 0 19. r = sec 0 csc 0 In Exercises 21–24 find…

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Q: Use sine and cosine to parametrize the intersection of the cylinders x + y = 81 and x? + z? = 81.

A: Find your answer below

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 - y³)żdy

A: Given integral ∫b2y6-y812dy The objective is to evaluate the integral by trigonometric substitution.

Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: Let fcxry)= 2X sinly)+3X Cos CY ). Find the tangent Plane at the point 2,0).Use the tangent Plane to…

A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: Given f(x, y) = 6e sin(2y) %3D Question Help: OVideo

A: We need to find del function at given points.

Q: (Sece tana) Sec de Cot e Cos?0

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: 20. Find given that a) y = arctan ) simplifying your answer as much as possible, b) y = In(x'-3x? +…

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Q: cos(2z) dz c = |Z| = 1 Evaluate where at oriented 5-4 cos(z) counterclockwise?

A: Let fz=cos2z5-4cosz Singularities of f are those points where the denominator is zero. So, put…

Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: Find the surface area of the figure generated by revolving x = 6 cos(t), y = 6 sin(t) where 0 <ts…

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Q: 5s F(s) %3D (s + 7) (s? + 4) 35 35 10 -7t Answer: f(t) G, cos2t + sin2t) 53 %3D 53 33

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

Q: Determine the so luti'on of the equertion: dy dx2y cot x= 1- 2xcot 2x- 2csc 2x

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Q: Finat edt roots of CTeetion? Sinz=D Complex Aumber 2l Sin z=i Sinh

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Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: Let R=[a,b]×[c,d]. || e*sinyda = e*dx S siny R. C Select one: O True False

A: This is a problem related to double integration. Based on the general formula and concept we will…

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

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&lt;0 and we need to prove that | eiz | &gt;1 For b part, we need…

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

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Q: Selve the boundaly value preblem (D+ 36)g = and y'(o) = 2 that yte=I Sin 6x, given %3D

A: We know, 1D2+a2sin ax = x2∫sin ax dx

Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: Teorema de residuos: muestre que z=0 es un cero de orden 2 de 1-cos(z)

A: To show that z=0 is the zero of order 2 of the function  fz=1-cosz

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: Find dy Sor The Sullowing Suetien? ) y = Cot 2) y = Ln [cosx) %3D

A: Please refer to the image below.

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: Evaluate. S cos z In(sec z)dz Your Answer: In(sec z) sin - In tan z + sec + sin z + C

A: Please see the answer below.

Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

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Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

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Q: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.