Two linearly independent functions f(x), g(x) E span{e® ,1+ x², cos(x)} satisfying f(0) = g(0) = 0.

Q: Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions.

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Q: Suppose f and g are differential functions with the values given below. f(x) f'(x) g(x) g'(x) 1 1 3…

A: The answer is found in step-2

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

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Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

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Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

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Q: Example 7. Show that T: E2 → E2, defined by is not linear T((x₁, x₂)) = (x₁ + x2, x1 - x₂ +1)

A: as we now for a linear map T(01 ) = 02  where 01 is zero of domain and 02 is zero of codomain

Q: 3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D…

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Q: 5. Find the linearization, L (x) f (a) + f' (a) (x – . a) of the given function "f" at "a". %3D - f…

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Q: Find lim e x2 dt X 00 0. ej

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Q: Given for C[-1,1] the inner-product function (f,g)= | f(x)g(x)dx , find |F|| if f(x) =1-3x.

A: The solution to the given question is explained below.

Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X & Y are independent then we say that…

Q: Suppose (0) (ii) (iii) X, has a pdf f(x₁) = x₁²e-x²³/ 16 0 X₂ has a pdf f₂(x₂)=< $₂² 4 0 X, and X,…

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Q: Find the anti-derivative of g(x) = 2*, which contains the point (0, 2.44). ⒸG(x) = -2 O G(x) = 2 O…

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Q: Theorem 17-1. If T, is a consistent estimator of y(0) and y {y(0)} is a continuous function of y(0),…

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Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: Specify c-1, Co, Ci and p such that the formula c_1u(x – k) + cou(r) +cu(z+ k) u'(2) 2 denotes the…

A: This is a problem of Numerical Analysis.

Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: (3–x*) ane d 2x. Calculate the Wronskian of functions

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Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: find the values of C1 and C2 so that the given functions will satisfy the prescribed initial…

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Q: Use differentials and the graph of g′ to approximate                                        (a)…

A: From the graph g'(3)=3 Given that g(3)=8

Q: Determine if the following functions are linearly dependent or independent by determining their…

A: The Wronskian of a set of function y1, y2, y3 is defined as, If the Wronskian W is non-zero then…

Q: 1.)Integrate: ∫(x+1)(x+2)^6dx Group of answer choices a.)(2/56) (7x + 6)(x + 2)7 + C b.)(2/56)…

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Q: 10

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Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: 3. Let g(x) = V10- cos(x) +3x. %3D 3.1. Find g'(x). 3.2. Find the linear approximation to g(x) at x…

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Q: give an example of a function that is not a dirichlet function and justify

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Q: Two linearly independent functions f (x), g(x) E span{e* ,1+ x², cos(x)} satisfying f(0) = g(0) = 0.

A: Two functions are linearly independent if their wronskian not equal to zero for all x.

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: Given for C[-1,1] the inner-product function (f,g)= [ f(x)g(x)dx, find ||f|| if f(x) =1-3x.

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Q: Show that the functions In x , In(x2) linearly dependent (0, co) are on

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Q: 1)Differentiate the following f(x) = x³In (3x? – 2x + 7) esin (x) g(x) : x² – 1 h(x) = log,(x + 1) +…

A: " Since you have posted a question with multiple subparts, we will solve first three question for…

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: Find a function of the form y = Asin(kæ) +C or y = A cos(kr) + C whose graph matches the function…

A: Definition used -             Trigonometric function -                         y = Asin(kx)+C or y…

Q: 5.2-9. Determine the constant c such that f(x) cx (1 – x)°, 0 < x < 1, is a pdf. |-

A: Given: fx=cx3×1-x6        0&lt;x&lt;1

Q: 1. On (–1,1), two functions Y1 (x) = e2« cos x, y2(x) = e2ª sin x are linearly independent linearly…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x= 1 40 2.80 .CO .DO 0.

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Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.