If 1 Å : V(x2 + y?) [(хуz — Зху)а, + (zу? + 3x? )а, + ху а,] And B = r2 a, + sin 0 aø Find JÃ x B| at P (1,2,4)

Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: If 7=(x+1)√√x² + yi+tan (3x-y)j and g = y find: fxcurl g+(g.V) at (0,1,1) x + y In(xy+2)+ i+…

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Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: Find 1 2 – if | - Əx y,z w = x2 +y – z + sin t and x+у %3Dt

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: 14. If we let u = 4x – 1 for the (2tan(4x-1)-3 cos“(4x=1) dx. what will be the cos(4x-1) resulting…

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Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: Find all the roots, of 2=+1+V3j A =D/2 (cos +j sin-) - B z=V2 (cos (-+ka) +j sin ( + ka)), k=-1,0…

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Q: ,2 - 1 If z = cis 0, show that i tan 0. 22 +1

A: this is complex analysis question and also very lengthy questions so I can do it in advanced…

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

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Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

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Q: If sin u = 3/ 5 and sin v = 4/5 and that u and v  are  between  0 and π/2,               evaluate:…

A: Given: sinu = 35 ,  sinv = 45  u and v are between  0 and  π2  To evaluate: sin(u-v)

Q: -Prove that: y" = 1 if y=csc(tan")

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Q: show that1) d/dz [cosz] = -sin z

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Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

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Q: 10s¯ + 8s + 29 inverse laplace ( (2s 3s + 7)- -

A: We have to find the partial fraction first.

Q: 4. In triangle XYZ it is known that XY 1 YZ and sin X = cos Z. Which of the following must be true…

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Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: 4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y"…

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Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: Show that w°sin(xw) пе dw= 2 cosx if x > 0. w* + 4

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Q: If f(x) = 12sin(green wave), then the red wave isi %3D 20 |-3T/2 -TT T/2 TT 3h/2 2n |-10 IF f(X)=12…

A: Red wave satisfies the point -π2,0,3π2,0  a) Given,   6sinx+π+6 Put x=-π2…

Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: 3. If tan(a-iß) = x- iy , show that x? + y?-2ycoth2B = -1

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Q: Q# (17' Compute: [tan (10x)sec(10x)dx tan³ 1 tan(10x)+C 10 1 A) tan (10x) – 3 30 1 1 В) sec (10x)--…

A: We use substitution method to solve the Integral.