1-In (e) + In(2x) = In3 2- 4 log 2 – log3 + log16 = x 3-Expand In [x* sin' x /Vx2 + 1T] 4-if sin-10.6 = y find y and all six trigonometric functions from the following figure, find b, all six trigonometric functions of 0, and all six inverse trigonometric function of sin-ty 5 3 sin ly = 0

Q: Within the interval 0≤x≤ 2, the graph of sin a crosses the x-axis at three points: x = 0, π, 2.…

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Q: Differentiation#11

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Q: 3. If f(x) = x + sin(x) is a periodic function with period 2W, then a. It is an odd function which…

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Q: 21 Date... w******** Q. Find the Fourier Series od (x) = X -즐 <x<플

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Q: y = log (cos(2x) );y'=* %3D %3D O 2 tan ( 2x ) / In (10) O - 2 tan ( 2x ) / In (10) O 2 cot ( 2x ) /…

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Q: Let f (θ) = 2 sin 2θ + sin 4θ. (a) Show that θ is a critical point if cos 4θ = −cos 2θ. (b) Show,…

A: “Hey, since there are multiple sub-parts posted, we will answer first 3 sub-parts. If you want any…

Q: x2 – 1 if æ <1 1 f(x) = T In a a cos 2rx + b sin( 4 In 2 if 1<a < 4 2" – x2 if 4 < x - where a and b…

A: For f(x) to be continuous at x = a : LHL= RHL = Value of the function at x = a

Q: Consider the family of functions h(t) = cos(3.0t) + 1.5 cos(3.6t) + 2.0 cos(vt) for various values…

A: The solution is given in the next steps below:

Q: 2. Consider the following periodic function and its Fourier series: 2 f(x) cos(nx) n? – 1 4 f(x) =…

A: Given periodic function is  fx=sinx for -π&lt;x&lt;π The Fourier series of the function fx is also…

Q: e-itH, (§, E) 1 exp (-it – (1- c2-0") (1 – e-rQ&») + 27Q¢,ns (1 – e2rQt,) (1 – e-2#Q¢,n) + 27Ql,ns…

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Q: O1/Find the Fourier series for the following periodic functions. + cos(x) + cos(3x) + 2 cos(5x) +...…

A: To find: The fourier series for the given periodic function.

Q: 2 cos t if 0 <t < 2, Consider the function of period 4, defined in the interval from -2 to 2 by g(t)…

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Q: Find the Fourier Sine Series for the following periodic functions 1 (sin(4x) + sin( sin(12x) +…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: I need the answer as soon as possible

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Q: 1+2 e-kt cos kx = k=1 sinh t - cosht cos x

A: To prove / disprove: 1+2∑k=1∞e-ktcoskx=sinhtcosht-cosx

Q: log, eln 5)(arccos(x)) simplifies to a) arccos(x) b) cos(x) c) None of these O d) 5 arccos(x) O e) 5…

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Q: Suppose w where 2+ sin(5t), and z = 2+ cos(3t). 5t I = ex, y A) Use the chain rule to find de as a…

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Q: Here we consider the 2n-periodic function f: R → R, that is given by f(2) = | sin()| for |æ| < . a)…

A: Let f:ℝ→ℝ be a 2π periodic function defined by fx=sinx4, x≤π To find the complex Fourier series of…

Q: 2. (a) Find Fourier Series representation of the function with period 27 defined by f(t)= sin (t/2).

A: Sol (a) Fourier series of function fx on interval -L≤ x≤ L is defined as: fx=A0+∑n=1∞…

Q: No. 2. X = principal root of no. 1; Y = second root of no. 1; and Z= third root of no. 1 Let: 13-j7…

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Q: 2. (a) Find Fourier Series representation of the function with period 2 defined by f(t)= sin (t/2).

A: The given problem is to find the Fourier series representation of the given periodic function with…

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&gt;0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: The function (f), even and periodic with period 4, is defined by: f(t) = 1 si te[0; 1[ f(1) = 2 – t…

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Q: 7. (a) Use Newton's method ONCE with an initial guess of ro = 0.1 to find an approxi- mation to the…

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Q: 3 Question 5 Example 6.4.2 of APEX Calculus uses this fact (which appears in an integral table): f…

A: The objective is to find the right option.

Q: 4. (a) Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. Find an…

A: We will use basic knowledge of ODEs to solve this question.

Q: In( cosh(3x)+sinh(3x) )= Select one: O 3 sinh(3 x )+ 3 cosh(3 x) O- 3x 01 zero None O 3x

A: Formula to be used sinh x = [ex– e-x]2cosh x = [ex+ e-x]2

Q: (a) Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. Find an integrating…

A: “Since you have asked multiple questions, we will solve the first question that has been asked. If…

Q: 12. Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. Find the root of f(x) = cos x + 2 sin x +x? by using Secant method. Let the initial value xo = 0…

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Q: 15. f(x) = for every x E (-4,3] x+4 16. f(x) = sin (2) in the interval x 2-2 3 17. f(x) = { 2 - x2…

A: As per our guide lines we are advised to solve only first question. Please kindly upload other…

Q: 4х-10 4.f (x) = log , when x = 3 X-6 Trigonometric 5.f(x) = cos(4x 6.f (x) – 10), when x = 4 3D sin…

A: 4. f3=log43-103-6=log12-10-3=log-23=log-23+iπ=log23+iπ=-0.1761+iπ

Q: 1. The graph of y=sin z is transformed so that the transformed image has a period of 4m and a phase…

A: Given problem:- The graph of y = sin x is transformed so that the transformed image has a period of…

Q: 3. The coefficients of the half-range sine expansion of the given function f(x) = 3 sin 2tx, for 0<x…

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Q: A string is stretched and fastened to two points at a distance 'x' of 10 cm. Vibration is started…

A: The given problem is to show the displacement of initial shape of the string from the given…

Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

Q: sinh (1+Inx)= Select one: ex-1 2xe O Zero e Inx 2 O None e?x² +1 2xe x² +1 O 1+ 2x

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Q: 1. Problem. Express the function f(x) e"/L (for 0 < x <L and assumed to be periodic with period L)…

A: Given:- Express the function f(x) = ex/L (for 0 ≤ x ≤ L and assumed to be periodic with period L) as…

Q: 5. Find the term representing the third har- monic for the periodic function of period 27 given by:…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: 14. Within the interval 0 ≤ x ≤ 27, the graph of sinx crosses the x-axis at three points: x = 0, π,…

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: A periodic function of period 2n is defined as -n < x < 0 0 <x< T — 2х, f(x) = { 2x, 2х, i) Sketch a…

A: We will use basic knowledge of Real analysis and Fourier expansion to answer both parts of this…

Q: The general solution of the equation = (1+²) cosx is y(x)=tan (C+ sin x). With the initial condition…

A: The given differential equation is dydx=(1+y2)cosx. To Find: y(0.4), y(0.5), y(0.6). Using Euler's…