-7/2 < x < 0 0 sx< T/2 (0, 10. f(x) = 3 cos x,

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Q: Find the critical points of the function f(x) = 11 + 4cos(x) + cos(2x).

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A:

Q: Given t2 – 1 dt 1 + cos²(t) At what value of x does the local max of f(x) occur? f(x): %3D

A: Part 1 of the Fundamental Theorem of Calculus : If  f(x) = ∫axg(t) dt then  f'(x)= g(x)

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A: This question is based on chain rule differentiation and indefinite integral.

Q: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

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Q: Q1\ Determine all the critical points for the following:- f(x) = sin?x - cosx On the interval…

A: Differentiation of the function helps to find the critical point. Differentiation of the function…

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: 1 The value of S dx at x=0 is sinx+cosx C V7 (Inv2+1) +c Cn|vZ+ 1] +c ㅇ글미VZ+ 1| + c c -공in(V2+ 1) +…

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Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

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Q: Find all local minimum and local maximum value(s) of the function. f(x) = 2 cos x – sin? x, 0< x< 27…

A: Option 4

Q: 1. Prove: a. S csch x = In|+ c b. S sech x = 2 Arctan(e*) + c

A: *As per the guidelines, only the first question is supposed to be solved. Please repost remaining…

Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: 10. Does there exist a harmonic function in z| < 1 taking the value 1 everywhere on |2| = 1? Is your…

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Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

A:

Q: ii. Verify that the u = -e-Y tany is harmonic in an appropriate domain D.

A: Given that u=-e-ytany.  If u is harmonic then uxx+uyy=0.

Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

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A: Given, function

Q: @) skelch a graph of the Punehion y=sinx-sinsx at Le,zn] 4) Given Secanda -10 and sr casd x =3,…

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Q: Given that f is a periodic function of period 4 S x?, 0 sx< 2 and that (x) = {x + 2, 2 5 × < 4' then…

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Q: Find a possible formula of the form A sin t+k or A cos t+k for the periodic function with midline y…

A: The standard equation of any sinusoidal curve is given by  y=Asin(B(t-C))+D      or…

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Q: Evaluate L{e* (cos at – sin nt s+3 A. (s+3)° – n² (s+3)² - – n² 2 S - 3 (s – 3)° – n² (s-3)° -R 2 2…

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Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

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Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: - 19. Is f (x) = sinx a periodic function if so, find its period ?

A: Introduction :

Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: - Show that the following functions satisfies the heat oquation = . (e>0, constant). 1)2 =e sin .…

A: Since you have posted multiple questions, but according to guidelines we will solve first question…

Q: Given +2 – 25 dt 1+ cos2(t) f(x) : At what value of x does the local max of f(x) occur? Preview

A: Consider the given function.

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Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = sin- x + 0 x = 0

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Q: 36 - With p0=0.5 and p1=pi/4 starting point f(x)=cosx-x, find its root when n=0 using Secant Method.…

A: Given: To find the root of the following equation using secant method, f(x)=cos(x)-x Initial points:…

Q: Consider the graph of f (0) = sin(20) on the interval 0 <0 < 2ñ . What are the critical values of f…

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Q: By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the…

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Q: Let cos 0 + (sin 0)2 with 0 <0 < 2T. Determine any critical points of y on this interval.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.