12л Approximate sin by using a linear approximation with f (x) = sin x. 13 12л sin z f(a) + f ' (a)·h = c, where 13 a = h = с 3 (Note that these are numerical answers. No letters can be used in an answer.)

Q: ди 4. Solve = a given that (i) u = 0 when x = 0 and x = l for all t at (ii) u = 3 sin TT X when t =…

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Q: π/4 1 π/4 sin TX cos 2y sin 4z dy dx dz = 0 0 0 (Type an exact answer, using n as needed.)

A: Solution

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Q: 14. Find the antiderivative of 5sinx In 5 cosx. a. 5cosx +3 c. 5sin x In b. 5sinx-2 d. 5 sin x + 7…

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Q: 57. The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin 21 m/sec for all…

A: We will use the definite integral to find the value of ' s '.

Q: 4. (a) Find a seventh-degree Maclaurin approximation for f(x)=sin x. sint dt (b) Use your answer to…

A: We will first consider the given function. a. The objective is to find the maclaurian approximation…

Q: 1.4 1. Calculate an approximate value of the integral So5 (sinx – Inx + e*) dx by dividing the…

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Q: 4. Let f(x) x² + cos(Tr). f&)= Qx -Tsin(Tx) (a) Use Newton's method to find the root of f(x) with x1…

A: a) Given f(x)=x2+cosπx  with x1=-12=-0.5    f'(x)=2x-πsinπx  we know Newton's formula to find…

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A: Here, the given function is: g(y)=cos(y+1) To find the linear approximation of g(y) at y=y0=0 using…

Q: 7. Given a positive constant k, the most appropriate initial substitution for Vx² – k -dx is: a. x=…

A: Given that: ∫x2-kxdx

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A: Given integral is ∫01cost2dt

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Q: 3. L [f(3t)] if f(t) = e-³t+3³ sin3+ 4. f(t) = e-4tt(3sin2t - 2cos2t) 5. L [e-4tf(4t)] if f(t) = t³…

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Q: 9. The position of a moving particle as a function of time is given by: x = (4 - 0.11) sin(0.81)…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 1. a) For 0<x<1, show that /2 1+ x b) Use the estimate in a) and integrate it to prove that 1 1 -dx…

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Q: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

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Q: II. Let f(x) = e² sinx 1. Use the local linear approximation of ƒ at x = 0 to approximate e2…

A: Introduction: The formula of local linear approximation of the function f(x) is given by,…

Q: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

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Q: Find the critical numbers for the function f(0) = 2 cos 0 + sin? 0 for 0 < 0 < 2T.

A: A critical number of the function f is s number c is the domain of f that either f'(c)=0 or f"(c)…

Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: nd the definite intergral upper 1 lower 1/2 sin-1(x)/ square toot 1-x2 dx

A: Integrate ∫121sin-1x1-x2dx                          ......................(1) Put sin-1x=t…

Q: = In(2- sin z) with Given sin z + e -2 0. Using the rearrangement z z0 = 0.5. what is the value of…

A: The fixed point iteration method is a step-by-step method to find the approximate solution of the…

Q: 7. Determine the lowest positive root of f(x) = 7 sin(x) e-* - 1: a. Using Secant Method with…

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Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

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Q: Use differentials to estimate sin(0.1).

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Q: f (x) = cos(3r)[2 + sin(3r)]* on 0, O e*(16) - e*(7) O e*(-16) - e*(7) ) 1.52x10*(-4) O In100 - 9 O…

A: ∫avg=1b-a∫ab(cos3x)(2+sin(3x))4  ∫avg= 1π6-0∫0π/6cos3x2+sin(3x)4 dx        ....(1) Now to calculate…

Q: 3. Use Newton's Method to approximate the positive zero of f(x) = e* – 2 cos(x). Xo = 0 X1 = X2 = X3…

A: Answer is below

Q: * (s in-(x))² dx = V1-x2 Select one: а. sin-(x) + C 1 - x? b. (sin-(x))³ + C 3 C. sin-V1 - x²) +C O…

A: With the help of substitution method, integration is solved.

Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: ** The definite integral " - 1/4 • 1/4 tan-1x² + /x²+ 1 Cosx +2 dx is equal to A 1 • T1/4…

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Q: 9x²– e2x 2 Given by a function of x is equal to v1 – cos²x + where f(x) 3x+ e* = 0. find the roots…

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Q: 50. Find a real root of f(x) =x sin.x+ cos x = 0 by Newton Raphson method.

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Q: 19. (a) Find the approximations Tâ and Mg for the S cos(x?) dx. (b) Estimate the errors in the…

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Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

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Q: 1 dt, where g(x) cos x If f(x) = g(x) [1 + sin(t²)] dt, find f'(7/2) %3D /1 + 8 Select one: 21 sin…

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Q: 2 sin x Verify whether the function g(x) =1- is the solution of the integral equation [1 – (7/2)]…

A: The integral equation gx-∫0πcosx+tgtdt=1 is a Fredholm integral equation. We have to check whether…

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: Q2:A/ Evaluate the integrals 1/x sec (1 + e) tan (1 + e) dx Q2:B/ Find dy/dx Vidt sin x cos t dt 2

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Q: 3. Jlgu * Solve the D. E. to the I. V. P. sinx(e + 1)x- cosx - 1, y(0) =0 In (1 + cos x) =I+e O…

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Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e" = ex. Take x1 =…

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Q: 13. e-2t cosh³ 2t 14. cosh at cos at V3 t 15. sinh sin: 2

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: 28. Use Newton's Method to find the fourth approximation x4 the solution of the equation cosx =x…

A: we have to find fourth approximation using newton refson method.

Q: 10 - S sin(8a) arctan(sin 4x)da integralinin değeri aşağıdakilerden hangisidir? 9118002 8(T – 2) a)…

A: Given that  The integral  To evaluate the integral

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A: If you like the solution then please give it a thumbs up.... The Answer is:   1 . substitution…

Q: 2. By using Simpson's rule with N = 4,8, and 16 Integrate the following functions SOLVE PART B eX…

A: We need to use Simpson's rule to evaluate the integral. So, we need to find ∫0π4Tan X dX If we need…