If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

Q: Solve the following Bernoulli's D.E.: dy 3 „y = x*y3 1 %3D dx

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Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: 3. Evaluate in terms of gamma function: T'e

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Q: 2 lim In (cos x)e

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Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

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Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: Find dy for the following func tion s -니 y=(1+ cos zt)

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Q: In(x²+x)-In x+eln 4 dx In e(x+1)

A: Given integral, ∫lnx2+x-lnx+eln4ln ex+1dx

Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: ) prove thaE cos ( x) dx =- T e x" + x2 +l 213

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Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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Q: 1. Use the substitution method to evaluate x² S. VAI ³ + 50° dx

A: Here we have to find the integral using substitution method.

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: .2 -dædy In (x) ey

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Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: 7. If aatiß = (x + iyy*4, a>0, prove that %3D (i) a = 5 log, (x + y) -q tan log, e- loga (r + y) =…

A: The given isaα+iβ=x+iyp+iq,a>0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x).…

A: Our Objective is to find the derivative.

Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: d 5. Prove (arccot(x)) dx -1 Be sure to provide a written justification for your work. 1+ x?

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Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

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Q: 9-x 4. Evaluate ſ, S sin(x² + y²) dy dx

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Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: 2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for…

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Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: I need solution to this problem.

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Q: 11. Find L{tU(t - 1)} A. В. е ers C. D. e-s 1 E. None --

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Q: Find the general form of the antiderivative of g(x) = - cos4x

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Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: In (6x) to x if y = sin (5e') dt.

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Q: In 1 & 2 find dz/dx by the chain rule and also by rewriting z. 2 = (3x) z = /1- cos?x 1. 2.

A: Let's find.

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: 1.) Evaluate In 2 e*2arctan e* 1.)J1+e2x) sec(2arctan e*)" dx

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Q: ons z = sin y arn

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Q: 1.) Evaluate In 2 e*2arctan e* A.) Jū+e2x) sec(2ªrctan e*) dx

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Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: prove using the IVT. e^x + ln x = 0 has a solution.

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.