a) Functions y1, y2,., Yn are said to be linearly independent on an interval I if the equation c1y1 + c2y2 + +CnYn = 0 has only a trivial solution, namely c = c2 = .. = Cn = 0 on I. By using the definition, determine whether or not y1 = sin 3x and y2 = cos 3x are linearly independent for all of x. Then, show that these functions are solutions for the following equation. d²y + 9y = 0 dx2

Q: pu. --s) 4) Show that the function + and on the portion r <-4 of the real axis. is analytic…

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A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

Q: ƒ'''' (x;): = f (x₁+2) — 4f(x₁+1) + 6ƒ (x;) — 4ƒ (x;_₁) + f(x;_₂) - - hª

A: We have to prove f''''x=fxi+2-4fxi+1+6fxi-4fxi-1+fxi-2h4…

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Q: Test the sets of functions for linear in­dependence in F For those that are linearly dependent,…

A: Given: A set of functions is 1 , sin2x , cos2x. To Find: If the given set of functions are linearly…

Q: Q1/: a: Using the relation showthat Jv2 (x) =, cos x

A: See the attachment

Q: Given the functions Az) = cos(x) and g(z) = x - 5x- 6, determine the domain of the combined fx)…

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Q: The interval(s) that contains the root(s) of the equation below is/are: cos +x² – 3x = 0 A. (-2,2) &…

A: Let's find.

Q: B)Is w = Ze² analytical function or not?

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Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = 1

A: The given functions are, f(x)=sin2x, g(x)=cos2x, h(x)=1. To Check: Whether the function h(x)=1 is in…

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A: Let B={sin2x,1-cos(2x)}.

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Q: Let Ax,y) = 5x + 5xy – 6y. Give the coordinates of a point on the graph of f at the point (3,6). O…

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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: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

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A: y=(5x+4)3

Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

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A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: 1. Consider the function: x3 − 6x2 +11x − 6. This function has three roots at x* = 1, 2, 3. 1. a)…

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Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: Let f(z) : D C be a complex function. Is it possible for both f(2) and f(z) to be analytic? 2. • If…

A: Solution

Q: Determine two funetions f and g whose produet result in (f x g)(=) – 8 sin"I+ 27.

A: see below the answer no need of explanation

Q: Let z = tan² (3x²y2²). Find Vz. O Vz= 12xy² tan (3x²y²)sec² (3x²y²)i + 12x²y tan (3x²y²)sec²…

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Q: f(2) =2x² + y+i(y² – x)

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: If the equations x = u? - v and y = 2uv define u and v as functions of x and y, find and %3D O A. du…

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