fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13 sin(1) Oel 3x2 sin x x' cos x 近。 N

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: tan z, + tanz, = T-(tan z;) +(tan 72) tan(z, +2) ) Prove that: cos(z + w) = cosz cosw + sinz sin w

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Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: The suitable substitution to evaluate the integral /tan°(2x) dx is cos“(2x) O u= tan(2x) O u=…

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Differentiate y = In (sin + cos ) cos -sin 2r Va(sin a + cos V") sin E + cos E 2r V(sin a + cos a)…

A: we will apply, chain rule: ddxf(g(x))=ddg(x)(f(g(x)))×ddx(g(x)) Sum rule:…

Q: The suitable substitution to evaluate the integral tan°(2x) dx is cos“(2x) u = cot(2x) • u= tan(2x)…

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

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Q: You have to determine fi(x) = /x + Vx • f2(x) = cosv1 + x² 1+|sinx| • f3(x) = contnuty and chek aslo…

A: Continuity of a function: A function f(x) is said to be continuous at x=a if limx→a f(x)=f(a)  A…

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

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Q: Let a, b be real numbers and consider the integral (ax² + b) cos(x)dx. Using integration by parts…

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Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: What is the integrable form of sin-cos-sin0 d0? 2 A /1 – u² du B Vu²-1 du © : fcomndn cosu du D sinu…

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Q: What substitution should be used to solve the integral S O sin u=3x/2 O sec u =2x/3 O sec u =3x/2 O…

A: Evaluate the integral by using substitution method

Q: In A XYZ, ZZ is a right angle and mZX = 53°. Which statement is true O cos 53* YZ %3D XY XZ O tan…

A: From the given figure representative diagram is shown below:   With respect to ∠53°.…

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

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Q: cos ve J Vē sin? ve de = 2 sin ve 1 jus O 2 + c sin ve

A: Given ∫(cos(√θ)/√θsin2√θ)dθ   Let √θ= t     Integrate on both sides     (1/2√θ)dθ= dt            dθ=…

Q: а. х %3 (3, —4,0, у b. х %3D (2, 1, —3, 4y c. x = (sen k, cos k, 24y para un entero positivo fijok

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

A: We have to use derivative definition.

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: If f(z) = 1+ sin z %3D Then d 1+ sin z = sec z (1+ tan z) COS Z zp cos z

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Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: Compute 4 sin(TTX) d dx A. 4 sin(TTX) B. 4sin(TTX) In4 C. 4sin(x) (πIn4).cos(TTX) D. 4 sin(TTX)…

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Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

A: Given: ∫tan52xcos42xdx

Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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

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Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: Which of the following is true? A Jsin(3x)cos(4x)dx= [ Sin(7x) – sin(x) Jcos(3x)cos(4x)dx= [cos(x) +…

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Q: Compute Cos (x + k ) cos a dx by using substitution technique where k is a constant. [Hint: cos(A±…

A: The given integral is cos(x+k)/cosx.

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

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

A: solution

Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

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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: 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: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2>0 then…

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz

Q: Integrate the trig identity 2 cos j x cos kx = cos(j + k )x + cos(j -k )x to show that cos j x is…

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