Make the orthagonal set of functions {1, cos(x), cos(2x), ...} orthonormal on the interval [0,2pi].

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: Consider the function f (x) = x + cos x a) Find the x-value(s) (if any) for which f(x) has local…

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Q: Use function f Gx)= X-cos(x) to %3D differedtinte Newton's fined Poird method and methed.

A: Given that f(x)=x-cosx The newton method is, xn+1=xn-f(xn)f'(xn) Then f'(xn)=1+sin x So, the…

Q: What is the range of the function f(x) = 2 cos x + 1? [0,3] O[-2,2] O[-2, 1] O[-3,0] O[-1,3]

A: f(x)=2cosx+1

Q: What is the necessary condition of analytic function ? Find the singular points of the function f (…

A: Necessary condition For a function f(z)=f(x+iy)=u(x,y)+iv(x,y) to be analytic is that it must…

Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

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Q: -1 What is the range of the function y = cos ( +1)? 이[-2,이 O [0, T| T o (0, 7)

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Q: what is the absolute extrema point(s) of f(x) = e1-cosx on [ -pi/2 , pi ], if there are any?

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Q: Find div F and curl F if F(x, y, z) = 2eyi- 7 cos y j + 4 sin² z k. div F= curl F=

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Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: Differentiate the following function 3 U = ²³² √² + ² + 2 u= +2√+³

A: Derivate with respect to t

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

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Q: Show thatI cos ve (-1/4s)

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Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: 4) dependent Show that the following set of functions is Linearly independent or linearly f₂(x) = 3,…

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Q: What is the domain of f(x)=cos-'(In(x))? Select one: O (0,1) O (0,0) O (0,e]

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Q: Let f = -2x² + 5y² where x cos(t) and y = sin(t). af Ət using the chain rule. Write your answer as a…

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Q: Let f(x) = (8 sin z + 2 cos z)tan f'(z) -

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Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

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Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

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Q: What are the maximum and minimum values of f(x) = x + 2 cos x on the [0, π] interval

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Q: one of the following pairs of functions are orthogonal on interval [-1, 1] Select one: x.cosx b. x,X…

A: Given the interval [-π,π] and the pair of function. a. x2,cosxb. x,x c. sinx,xd. NOTe. sinx,cosx We…