6. Let f(r) = -a cosr. With po = -1 and p1 = 0, find p3; %3D

Q: 1 13. Which of the following is an antiderivative of the function f(r) = 5+x? A. 2r In(5+ r2) B. C.…

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Q: 13. What is 2sinx cos x dx? TRONG A. +C In 2 C. 2 cos.x B. +C 2sinx In 2 D. In 2 14. Which of the…

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

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Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

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Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

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Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: For which values of a does x + a = 0 have a solu­tion in Z5?

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

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Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

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Q: 2 /2 L(x)=- I Jo cosh(x sin 0)d0. Use the composite Simpson's 1/3 rule with step length h = T1/16 to…

A: Use the composite Simpson's 1/3 rule ∫abf(x)dx≈∆x3fx0+4fx1+2fx2+4fx3+  ...   4fxn-1+f(xn) here…

Q: 2. Find S'and S" for the function: S = + 2t2. Cos(t)

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Q: IV. Suppose z is a function of x and y, and tan yy² + x² = z*e6y. Solve for dz dz and

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Q: 6. The value of S,2 esinx dx, by using Simpson's 3/g th rule is equal to (A) 2.09323 (B) 2.19323 (C)…

A: Option D is true.

Q: Calculate SN given by Simpson’s Rule for the value of N indicated.

A: In this Rule, N is an even number and h = (b – a) / N. The y values are the function estimated at…

Q: if M Z- Sin (xy) fined 4 22 y= lint t-1

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

Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: Find an antiderivative of the given function. 7 cos 2x

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Q: Consider the figure below. uestion 1 T. 2x W Зх - 5 Previous

A: Given TW= 2x, 3x-5

Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: 1. Find the following antiderivatives: (b) (cos(5e) - sin(21)) dt eat (c) -2t dt 2

A: As per guideline we have to solve only three

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

A: A differential equation is an equation that relates the variable and it's derivatives. Solution of…

Q: 3. How would you classify AG? A J G

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: 1. By using the following data compute the Karl Pearson's coeficient of corelation. EX=250, EXT =30,…

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

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Q: Ernd the area of the shaded rearon o the r= cos 2A 01011 4 1 0--1- 7ven ST 041 112 1世學1S 01ル 6. 10…

A: The equation of the curve is r=cos2θ.

Q: s+3 is equal to s2 – 6s + 45 | A e3tcos6t В e3t (cos6t + sin6t) © e-3t(cos6t + sin6t) D e3t(cosh6t +…

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Q: Solve the following Bernoulli's D.E.: dy +y%3D dr+y =x²y² dx

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Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

A: Simpson's rule error bound    Es≤kb-a5180n4 , where f4(x)≤k where ∣E​S​​∣  this e absolute values of…

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: Find k so that dx = ke" + C.

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Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: Find the G.S. about xo = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0 ||

A: Given DE is  (x2+4)y"+2xy'-12y=0 Given point x0=0 is an ordinary point.

Q: Solve the following non-homogeneous linear ODE of first order dy 2y + dx sin x

A: Given, dydx+2xy=sinxx To solve the above differential equation.

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: 3ey , find Given z = dz dz au

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Q: terms HK K . J 12 in

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Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: Q2/ Find dy/dx for the following functions: x4 In x - 16 1. у%3D (ln x)3 2. У 4 3. у %3D0 (sin (In6)…

A: y = (ln x)3 To find the derivative (dy/dx) or the given expression we will use chain rule. Chain…

Q: The linear approximation to fix) = E at x = 8 is given by O a. 2 - x Ob. 2 Od. 12

A: Given: f(x)= x3 Linear approximation of a function fx is given by the formula  y=fa+f'ax-a

Q: a) the linear approxinma ion to the function + 3X ät

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Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦

A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14

Q: 8. The area of the region outside the curve r = 3 - 3 cos 0 and insider = 6 is

A: We have to represent the required area first.

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

A: