Find the exact value of each of the following under the given conditions below. 4 T 1

Q: 1. Which of the following functions are in L¹? in L²? 1 a. sin x |x|3/2 b. (1+x²)-1/2 x²-1 d. 1 -…

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Q: 1. Determine the absolute extrema of f(x) = (sin r – 1) cos r on 2 2 if they exist, and identify the…

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Q: 5. Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos…

A: In the given problem we used the fact that f is harmonic on the unit circle, and using the…

Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2x. 3π b) In the interval 프 <x< 4 one…

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Q: Find one of the roots smaller than 5 of the following equation given below by la) using graph of the…

A: Function is…

Q: 4- Using the data sin(0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin…

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Q: Find all values of 0 in the interval [0°,360°) that have the given function value. /2 sin 0 = 2

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Q: 4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

A: This integration can be integrated by using substitution method. Clearly it is observable that put…

Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

Q: Refer to the graphs to explain why the equation sinh x = t has a unique solution for every t and why…

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Q: Q1. Find one of the roots smaller than 5 of the following equation given below by using graph of the…

A: We draw graph of given function when a=7. And then find the roots below 5 by observing the graph.…

Q: 2 Find the maximum and minimum values for f(x) = . Determine the -4 + cos x+ V3 sin x angles at…

A: Consider the  given function fx=2-4+cos x+3  sin x The value of the function at the endpoints of the…

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

A: Given formula is: A sin t + k or A cos t + k

Q: f(A) is an odd function, and deduce that for each x E R the value of the c) Show that integral 3A…

A: From part (a), the function f⏞λ is defined by f⏞λ=i2π3λcos3λ-1λ2sin3λ Relacing λ by -λ,…

Q: Show that the functions have local extremevalues at the given values of θ, and say which kind of…

A: Consider the given function is h(θ)=3cosθ2 for the range 0≤θ≤2π. The first derivative of the…

Q: The approximation of /= cos(x³ + 5) dx using composite Simpson's rule with n=3 is: 3.25498 0.01259 O…

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Q: The periodic function with L=2 is presented as f(x)= 0 if -1<x<0 and f(x)= x if 0<x<1. Find the…

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Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: 2) Give a big-Oh estimate, O(x³), for the function f(x) = (1 + 2x + 2cosx + 2r*)(log x² + 3lx| + sin…

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

Q: 3. S(5 cos x +4 sin x) dx

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Q: 2. Let f(x) = 3 cos 2x + sinx. a) b) Show that f'(x) = -5 sin 2x. π 3π In the interval <x< one…

A: We need to find derivative and normal.

Q: Evaluate the given function tan?ydy = sin3 xdx is equal to. 30 3(tany – y) А. Зх + cos³x = cosx cosx…

A: tan2ydy=sin3xdxIntegrate both sides and solve.

Q: 4 Using n = 8 approximate the value of cos (1+ ya) dx using Using Trapezoid rule, and Display the…

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Q: 2. Find all values of 0 in the interval [0°, 360°) that have the given function value tan 0 = -V3.

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Q: For each of the following, find dy: cos (e-*)+1 1. у 3 1-cosh (1–x) 2. y = 21+x'Arctanx

A: we have to find derivative

Q: 4. Which of the following functions has the largest period? a. f(x) b. f(x) c. f(x) = = = sin(2x…

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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: Find all values of 0 in the interval [0°,360°) that have the given function value. tan 0= 3

A: Given, tan theta= sqrt(3)/3= sqrt(3)/(sqrt(3)×sqrt(3)) tan theta= 1/sqrt(3) [0°,360°)

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: In each of the following eliminate the arbitrary constants. a. -3x'y=c b. x= Asin(et + B) : x=c, cos…

A: According to our Bartleby  Q/A guidelines we are only allowed to solve the first subparts. Please…

Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

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Q: 2. For the function f(x) : = sin x. Show with the aid of the elementary formula. 1 1 (1- cos 2A)…

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Q: Given: y = sinh(ln(cos a)); Find y'. O (E) None of these O tan(x) sinh(In(cos x)) O sinh(ln(cos r))…

A: Given y=sinhlncosx To find y':

Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

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Q: 2. Prove each of the following using identities, showing all work in the process. a. cos (x +) +sin…

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Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

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Q: 4. Find all the values of x, 0 < x< 2n, for which the following are true. a. sin x = 0 b. tan x = 0…

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Q: х If f(x) = cos(1? + 1) dt, then find f'(x). %3D Select one: O A. None of the others O B. sin(x + 1)…

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Q: d. Show that sin ž is exists or not? e. Verify that the derivatives of sinh z. f. Solve the value of…

A: The solution are next step

Q: Find the exact value of each of the following under the given conditions below. V3 <a<t; cos ß= ,…

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Q: Find y prime for y=(cos(x))^x

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Q: 1. Evaluate the following: 3 sin z la. Give the equation of the tangent line to the graph of at the…

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Q: 3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result…

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Q: (a) Find an approximate value for the integral / cos a dz using the Composite Simpson's rule with N…

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Q: 2. An object attached to a spring oscillates around a position and is represented by the function y…

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Q: 3. Find the O to the nearest degree if and with if cos 0= -0.8910 and Q II with 0<0<360°.

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