If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

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Q: True or False: If we use substitution the substitution x = tan 0, then, the integral dx 1 + x2…

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Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: find integral sec 3 x dx

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Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

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Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: Use Property 8 to estimate the value of the integral.

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Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: we have to check the DE sin(x) +y cos(x) = 1 for Exact then My= dx None of These - sin(x) sin(x)…

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Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

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Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: S tanʼx dx

A: Answer is given in next step.

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: Suppose f(x, y) = / tan(x) + y and u = (-3,0). Then, Du f(-0.8, 8) =

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Q: 3 sec x tan xdx

A: ∫π4π3secx tanx dx

Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: when

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Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: 1 Integrate: S tan*÷x dx 3

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x*+20x-126x + 2x +3 dx…

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Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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