Let - (sin x cos y, COS I sin y, In). Compute div i

Q: If w = cos(xyz), compute for 82 w дудz

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Q: Let f(x) = 9 cos(sin(z°)). %3D Then f'(x),

A: Using the chain rule of differentiation,

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

A:

Q: 2 sin*x · cos³x dx

A: To evaluate ∫0π2 sin4x . cos3x dx using WALLIS formula.

Q: To compute sin (3t) cos" (3t) dt, first you need to I Select) * then subsitute u = [ Select ) * and…

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Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: I, (x, y) is any point on the __________ side of theta when in standard posi- tion, and r is the…

A: Complete the blanks in the statement.

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

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Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

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: Evaluate. de In(sin æ)] sin z cos z eCoS Z coS z COS T sin z esin z

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Q: V/ Prove that: (1) tanx= cot

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Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: 2 = using the relation r= VT show that sin x %3D EX II

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Q: Prove the following identities and show complete solution sin(u + v) + sin(u – v) = tan u cos(u + v)…

A: To prove the identity:sin(u+v)+sin(u-v)cos(u+v)+cos(u-v)=tanu Solution: We know:…

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

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: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

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Q: Evaluate et sin z cos z dr I COS using Simpson rule with h 20

A: Simpson rule  ∫abf(x)dx=h3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn-3)+2f(xn-2)+4f(xn-1)+f(xn) Where…

Q: 1. z, =1-j2 and Z,=2+j3; Evaluate cos[Z,J?

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Prove that sin (x +y) sin (x - y) tan x + tan y) %3D tan x – tan y

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Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: 2- Prove that: sin(z + w) = sin z cos w + cos z sin w %3D

A: sin(z+w) = sinz cosw + cosz sinw R.H.S  By multiplying 2 from numerator and denominator 1/2 (2sinz…

Q: HW /Prove that: (1) tanx=cot

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

Q: Prove the following identities. sin(u – v) 12. = cotv-cotu sinu sinv

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Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

A:

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…

A: Given force f(x)=x2-cos(3x)+2

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: Show that the following statement is true by transforming theleft side into the right side. cos…

A: We have to prove the statement: cos θ tan θ=sin θ We know that tan θ=sin θcos θ

Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: Evaluate: sin z dz +(°z – z)

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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: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

A:

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: on [ 0, 2î] ,determine all velafive the Finction. .If f(x) = sin x t cos X extrema for

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Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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

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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: sin(x + y) – sin(x – y) = 2 cos x sin y

A: sinx+y-sinx-y=sinx cosy+cosx siny-sinx cosy-cosx siny=sinx cosy+cosx siny-sinx cosy+cosx siny=cosx…

Q: Prove that: sin(z + w) = sin z cos w +

A: Here we have to prove that,

Q: a sin a + In v ) da + tan adv = 0 Cos a

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

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