1. Given : R]-1 GJ Cos20 Sin20 2sine coso sin20 Coso -2sin& cost |-sintcost Sint cost Cos-Sine Prove that [R]G[R]= [T] 1- --

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

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Q: Let ŕ ). ) - (0**) k (4 Sin 2+) + (4 cos 2 t, be the Position oF Perticle space in at time. Finc the…

A: The velocity is dr/dt and the acceleration is d2r/dt2

Q: 5. Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos…

A: In the given problem we used the fact that f is harmonic on the unit circle, and using the…

Q: Find the length L of the curve R(t) = -2 cos(5t) /+2 sin(5t) /+ tk over the interval [3, 6]. L =

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Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f (t)} for the following: F()=cos(V2 t)+ sin(3:) n(3t) b. =…

A: Given ft=cos2t+sin3t

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

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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: what is the absolute extrema point(s) of f(x) = e1-cosx on [ -pi/2 , pi ], if there are any?

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Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: A particle moves in the xy-plane in such a way that its path is defined by x = et cos t and y = et…

A: Given that, x=etcost, y=etsin2t. Differentiate x with respect to t, dxdt=etcost-etsint=etcost-sint…

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

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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: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

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Q: Having f (x) = 1 +e¬* sin(4x) and the interval [0,1] Apply composite Trapezoidal and Simpson's rules…

A: I have done by the direct method and trapezoidal rule and find the error by trapezoidal rule

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: GIVEN: f:0,2x]- -R, f(1) = sinz+ cos I %3D Find f (x) in factored form.

A: Differentiate the function fx with respect to x.

Q: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

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

A: We have to use derivative definition.

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

A: In both solutions i have used the definition

Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: What is the trigonometric substitution that you would use to evaluate the integral S V5x2 + 10x +…

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Q: Find the length of the curve [x = eª cos(t) y = et sin(t) for 04 (Hint: You can simplify the…

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: 2. Find the length of the asteroid x = cos't and y=sin't , 0<t<2n. x = cos' t y = sin³ t

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Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: 3. Determine any points of relative extrema of g(r) = 2 sin(x)- -r on 0, 271. %3D

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: ii. Verify that the u = -e-Y tany is harmonic in an appropriate domain D.

A: Given that u=-e-ytany.  If u is harmonic then uxx+uyy=0.

Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: 2x What formula would be used to calculate the right rectangle approximation of ²* (sin æ- cos x) dx…

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Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

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Q: ) Given that g(0)- 2sino - Scost, express g(0) in the form R sin(0 -A). giving values of R.

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: h) = 3 sin h (1-3x) cosh (1-3)

A: Given that hx=3sinh1-3x2cosh1-3x2 The objective is to find the derivative for h(x). The facts used…

Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: Find the points of inflection and discuss the concavity of f(x) = 2 cos (3x/2) on (0,2pi)

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

A: (1) Use the first principle to derive the derivative of cos(z),…

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: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: 16. So the maximum occurs at an angle of 0, but only if the angle is small enough. Explain why that…

A: Given: v=2μgscosθ+μsinθ Here μ is the coefficient of friction, g is the acceleration due to gravity…

Q: Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos (50)…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…