If f(x) =sin(x) then the Taylor's estimate R2(x) = .A sin(3) 6 .B _cos(?) X- .C cos(7) .D cos (3) 3.

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: 1. Find f' (0) given that f(x) = sinh-1 e*.

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Q: 2 lim In (cos x)e

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Q: Find the critical numbers of f(0) = 2 cos 0 + sin² 0.

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Q: What is the particular eq. of the given: y"+9y=e^x (cos 3x)+ x² + x³ex

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A: Given that f(x) = ln(cos3(2x+1)5)

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Q: 10) Find the linear approximation to g(y) = Cos(y+1) at y = 0. Use the linear approximation to…

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

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Q: 9) S(x.y) = sin (x-3y) Ans. .-2 sin(x-3y)cos(x-3y). S.--6sin(x-3y)cos(x-3y)

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Find the linear approximation of f(x)=cos(x) at x=3π/4 and use it to approximate cos(137∘). Give…

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Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

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Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 2 sin x f(x) = 1+2cos x Pvaluated at x = 1 ran

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

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Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

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Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

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Q: We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x).…

A: Our Objective is to find the derivative.

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: 9-x 4. Evaluate ſ, S sin(x² + y²) dy dx

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Q: Find the critical numbers of the function

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Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: (1) y = In(x+ 4)- x tan (2) xy + xy x + 3y (3) Iny e' sin

A: In this question we will use basic of calculus i.e concept of differentiation. We will simply…

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

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Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 19) Find [sin( x9+ 9x) ]' = _by Chain Rule A) 9x8sin ( x9+ 9x) C) 9(x8+1) cos x 19) B) -9 x sin (…

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Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: 8+ cos (9x) Perform a test to determine if -dx converges. 1/9 9 dx 1/9 (Type an exact answer, using…

A: Solution:- It is given that ∫π9∞8+cos(9x)x2dx is converges. we have to calculate ∫π/9∞9dxx2=?

Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: =1+ cos (x) x2 + 12x + 20 -dx 1 + cos² (x) 0. At what value of t does the local max of f(t) occur?

A: Given that f(t)=∫0tx2+12x+201+cos2 xdx To find the local maximum of f(t) at t:

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: 33 2Vx- f (x) (1–3t) (t³-8) T Sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x g(t) = t # 2 2-t

A: Given:

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental…

A: Given continuous time periodic signal is x(t)=2+cos2π3t+sin5π4t                            (1) The…

Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

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Q: (x2+ 1)(x tan 8 dx 81. dx 3) (x+2)3 dx (sin (sin (e*))) 83. (In (sec x tan x)) dr dx xex P (sin…

A: We’ll answer the first question since the exact one wasn’t specified.Please submit a new question…

Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.