Exercise 1: Show that the functions are orthogonal the indicated interval. a) f(x) = x, g(x)=x², x = [-2.2] c) f(x) = x, g(x) = cos 2x, z = [-/2, π/2] b) f(x)=e¹, g(x)=xe-e-², x = [0,2]

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

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Q: consider a function f, defined by f(x,y) = -y/√x2+y2   what is the behavior of f along the line…

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Q: Consider the function f(r) = (r – 1)e. a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0?…

A: Given, f(x) = (x-1)ex

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where…

A: Given that the tangent plane to the function f(x,y)=ln⁡(ax2y+bxy+c) is z=−6x−y−3 at the point…

Q: ) FIND F'6): c. f() - x 2- 3x2 F. f6) = VI-x

A: f(x)=x2-3x2differentiate w.r.t.…

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

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Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find derivatives of: 1.) f(t)= 7t          2.) g(x)= 3x-9      3.) h(v)= v3 4.) m(x)= π2

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Q: The domain of f(r) =tan(x) is Select one: a. 2 2 O b. IR - + nn} O c. IR O d. R {nt}

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Q: 6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c)…

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Q: PLS HELP ASAP ON ALL

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Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: 1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3,…

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Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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Q: Six)ax = [glu) du 1f flx): 3x-1 Solw) au ? Consider what is sec (3*) ·

A: we have to integrate