10. Prove the following formulas : d cot u = – csc u. dx d CSC и 3 — csc и.cot и. dx 2 du а ) * dx du b) dx du d 1 c ) cos -' u = dx 1- и? dx

Q: Plot along with its tangent r = -6ecos0 + 8 cos 40 in %3D 4

A: We knowx = rcosθy = rsinθGiven: r = -6ecosθ+8cos4θ                     Where θ∈0,2π     Hence, x =…

Q: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: Prove that (arccsc x) dx d d %3D (csc-1 x) = %3D - dx Ju/Vu2-1

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Q: 63; Evaluate the întegral +3 dx + 6xy dy where Cay Curve Joininy (t, -) to (16, I),

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: If y = atan (0) „x =a sec (0) prove or disprove d'y 3 cot(0) 4a dx

A: y =a tan3θ   ,   x = a sec2θ     'y' is a function of 'θ' and 'x' is also      a function of…

Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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Q: Suppose that a particle following the path (e' cos(t). sin(), ) flies off on a tangent at lo = 2.…

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Q: Compute Se (In(x + 5) – x²y) dx + (xy² + sin (e")) dy where C is the unit circle

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Q: S cos“C)dy

A: NOTE: Refresh your page if you can't see any equations. . take

Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: b) Describe, the motion of a particle with position (x,y) as t varies in' tthe given interval X= 5+…

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

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

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Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: dy let y = cos(In(cos(x))), then is dx

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Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Evaluate. S cos a In(secz)dr COS D

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Q: Y = = ecos(x) + cos(e*)

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Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

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Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: Grade: 107.5/156 Print Version dy sin(5æ) Find for y dx dy Preview ||

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Q: O sin (z)cos(z)dz

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Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: – Verify the following formulas : a) cosh u dx 1 du vuʻ-1 dx 1 du b) tanhu= ul<1 dx 1-u'dx

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 10. Prove the following formulas: du cot u %3D-сsc и. 2. а ) a dx d dx du csc u = - csc u.cot u. b)…

A: (a) ddxcot u=dducos usin u·dudx=dducos u×sin u-cos u×ddusin usin2 u·dudx=-sin u×sin u-cos u×cos…

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

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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: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

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: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: In(3) In(3) dx dy y/2

A: on solving this we get

Q: 2 [arc cos ( Incs-2) fdz ( Incs-z>) ] dz

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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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