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: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 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: for function f(x) = e=z²/(20²) sketch f(x)!

A: Topic :- Calculus

Q: 3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1…

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Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

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: Consider the function f(x) = In (x - 4) a.) Use the First Derivative Test or the Second Derivative…

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Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: b) Find the points at which the function f: C → C defined as: f(x + yi) = x - yi Have a complex…

A: To find the points at which the function f(x + yi) = x - yi has a complex derivative, we need to…

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 the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

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: 1 3. Given f (x) =-x + 4: 3 a) Determine the inverse. I 12] b) State the range of f (x). [ /1] c)…

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Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

A: The general form of the parametric equation of the curve in two-dimensional space is given by…

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

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: Justify whether the function f(z) = ze* satisfy the (C-R) equations or not. If it is an analytic…

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Q: PLS HELP ASAP ON ALL

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Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, ƒ'(1) = 1, g'(1) = 5. For the following…

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Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: (g/f)(x) f(g(x)) g(F(x)) f-1(x)

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: d (a) / ₁ (t²-1)²dt. -10 -10 (b)/(t²-1)²dt. (c) d dx 32² -10 3x² (t²-1)² dt. d (d) — (t²-1)²dt. dx…

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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: Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

A: Given: y'''-16y''+63y'=144ex y0=12 y'0=21 y''0=18 To find: Solution to the given differential…