:−² (sin 2t – 2ty) satisfy a Lipschitz conditi - = 2, -∞0 < y < ∞} in the variable y, also fir

Q: Q1: Find dy for the following a) y = tan-1(sinx) + In (sec2x) + 8tan5x + etn dx b) y = sec (x') +…

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: In (*-") l+V1-x2

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Q: All Sections 1) Solve the following equations for t Jy evt = 2) Find the derivative of y with…

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

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Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

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Q: PLS HELP ASAP ON ALL

A: 4. Given:f(x)=π2Getting the derivative, we have:f′(x)=dxd​(π2)Since π is a constant, the derivative,…

Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

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Q: Find, tan(x / 2)dx A) (1/2) sec (x/2)+c C) 2 sec (x/2)+c B) 2m sec(x/ 2)+c D) (1/2n sec(x/2) +c

A: Given that a integration of tan(x/2) and we solve it by using general formulas of integration. We…

Q: lim

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: sec'o, Q2: Ealate vtan 9-1

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Q: Let y= Sin x + 2 (05 X ) Ivaluate y, y'sy" and y'" at 4

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Q: ind the equation of the curve whose y" = ○ y=2 sin-¹ (2) — 4³-√3 -1 - O y = y = sin¯¹(x). X sin (x)…

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Q: sin (), x + 0 10. Find the value of K which makes f (x) K, x = 0 continues at x = 0.

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Q: 2. Use each of the Adams-Bashforth methods to approximate the solutions to the following…

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Q: Let / L sin(x +1) dr. The approximation of I using the two-point Gaussian quadrature formula is: O…

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Q: :(3:+a- (メ+) tanx tHany 1-tanx tany to

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Q13) {t+sin² t} = (A) + 1 [-] (D) 3 + 1 [-2] s²+4 (B) 3+ [4] (Ⓒ) + -] +4 (E) +-

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Q: Two waves on a string are given by the following functions: yı (x, 1) = 4 cos(20 – 30x) (cm) y2(x,…

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Q: 3) Find the Frenet (TNB) frame for the function at the point (2, 5n,0). Hint: once you find T and N,…

A: Given that  r(t)=-2cos3t,5t,2sin3t The formula for T is, T=r'r', Take the derivative for r,…