FUNCTIONS + INDICE 2018 J QI points where the curve meets the x-axis. (ii) Write down a suitable domain for the function f(x)=|(x+ 3)(x– 5)| such that f has an inverse. (b) The functions g and h are defined by g(x) = 3x – 1 for x > 1, h(x) = for x+0. (i) Find hg (x).

Q: 2. Use synthetic division to divide the first polynomial by the second. а. х2+x-3; х-1 b. 4x -Зx2 +…

A: a) x2+x-3 ; x-1  1  __| 1      1      -3            ↓      1       2    __________________…

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Q: b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) =…

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A: Suppose f(x) is a piecewise smooth function on a closed interval -c≤x≤c. The Fourier series of f(x)…

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Q: we consider the system 2r + 2y z+ 3y. dt For the given function Y(t) = (r(t), y(t)), determine if…

A: Since you asked for part 1, so I solved only part 1.

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Q: 1. Consider the quadric surface S2: + (y + 1)* . (z–3)² 4 3 (a) Find an equation for the trace of S2…

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Q: 5. Consider the tables of values for the two functions shown. _y =f(x) y = g(x) -27 -2 9. -1 4 -8 1…

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: The following f (t) is a periodic function of period T = 2n, defined over the period –T<t< n. S -2t…

A: We have to express the given function f(t) as a Fourier series expansion.

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Q: Consider the following recursive relationship defining the running time of t TA(1) = 0 TA(n) 3 TA) +…

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A: Let us considre the system of matrix Ax=b Using Cramer's rule, the solution of the system of…

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Q: Evaluate L1{ }. (s2 + 81) (s – 5) -

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Q: 12. Graph each polynomial function. leovlo a. P(x)= x(x² – 1) b. P(x)= x -6 c. P(x) =x* – 10x² + 6…

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Q: Let A be an m x n matrix over R. We define NA := {x € R" : Ax = 0}. Na is called the kernel of A and…

A: We can solve this using definition of kernel

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A: Solution :-

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A: Introduction: The process of modifying an existing graph, or graphed equation, to generate a version…

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Q: [4 10 In the matrix A = |2 2 -4 -1, suppose an is the pivot. This means that Row ? ♥ is being zeroed…

A: Given that A=410-525-12-47 To pivot the element a11, find matrix M such that M.A=Pivot matrix

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Q: а + 26 +3с- 2d %3 6 За +25-с + 2d - 4 2а -b - 2с-3а%3D2 2а- 3Ь +2с+ а 3D8

A: To solve given system of equations we use the gauss - Jordan elimination method.First of all we…

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Q: Q4/ Solve the differential equation a) xy. = 1+x + y+ xy dx

A: Solve the differential equation, by Variables separable method

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Q: (-1/3 2/3 2/3 2/3 -1/3 2/3 2/3 Exercise 1.1. Let M = 2/3 -1/3) This matrix describes a rotation of…

A: Given rotation matrix is M=-13232323-13232323-13.

Q: Let the curve C be traced by the vector-valued function Rt) = cos(rt) i + xt j + sin(rt) k. %3D

A: The vector valued functions are usually represented in the form: r→(t)=x(t)i^+y(t)j^+z(t)k^, where…

Q: 2 Determine the domain and range of the function y = Vx* + 10x + 24.

A: Domain is the values of x for which this function exist. Range is set of all the values that can…