Let zC LC and ZPOC ZP'O'C. 0" 0.

Q: Express z = 12 (cos 225° + isin 225°) into its exponential form. ww

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Q: (In n)2 5. an = 6. bn T = n sin Hint: Look for a way to use L'Hopital's Rule -

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: 1) y = 2sin (5x) ,2) y = In x'n cosh 5x ,3) xsin=14y = y tan-14x 4) y = ecosh (8x),5) y =- t +1 t…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: 7. Determine f(x) so that Scon cos(In°x)f(x) dx = sin(ln²x) + C 2 Inx (a) 2 In x (b) In x (c) (d) 2

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Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: 1 Suppose y = tan ¹æ. Then x = y tan Otan y Oarctan y

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Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 2 Find つえdy 2 こ( beny s)

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Q: 2(1-z) Evaluate S S --) dy dx dz

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Evaluate the integral.

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: Which of the following is true? @ Jcos(3x)cos(4x)dx= [ cos(x) + cos(7x) 2 BAll of the above ©…

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Q: In 8) * dx Integrate and evaluate the following

A: we have to integrate the following

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: Evaluate the integral 3 2x cos(xy)dydx 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: Suppose that w = x² + y² – z² | And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: Simplify w by substituting values of x , y and z and then solve the partial derivative.

Q: Compute Sinh Z c (az - z where C 121-1

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Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

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Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

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Q: Can you help with this problem step by step?

A: Given integral is

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: - 2+j= 5 Z153°.435, 3+ j2= V13 Z33°.69, and 1– j2 = /5 2-63°.435 (1 – j2) (-2+ j)(3+ j2) = 1.386…

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Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: If fex) cos cmx) dx = and %3D fox) E Coscn'x) then %3D COS n3 +! KIN

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Q: ons z = sin y arn

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

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

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

Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

A: 1. (a). To prove: ∫cschx=lnex-1ex+1+C Proof: We know that, sinhx=ex-e-x2 The left hand side can be…

Q: S az lnz (In z + 1)dz z In

A: ∫azlnzlnz+1 dz Put, z lnz=u⇒1·lnz+1z·z=dudz⇒lnz+1=dudz⇒lnz+1 dz=du

Q: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

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Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: 1) LtZ be a solukion (5) of complese mumber then the sinh Z+ Coah z -e is Z=1?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.