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

A: We have to find f and g which is the linear combination of given function satisfies f(0) =g(0) =0

Q: (a) Find if y = - (In z)*". (b) The function f(x) = (In z)* is an invertible function (you do not…

A: Given query is to find the derivative of the expression.

Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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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: Given a function f(x) that is continuous and differentiable, and a point a in its domain, we…

A: This question can be solve by taking approximation as x tends to a (more close)

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: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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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: f(x)=e^-5x at x=0

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Q: Find values of x, if any at which the given function is not continuous. SU) = x2-25

A: Hare we check whether the given function is continuous or not

Q: 4. Consider the logistic map f(x) = (1+ v6)x(1 – x) • Find the fixed point of 2-periodic cycle. •…

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

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Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

A: Solve the following

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: 1. Consider the function f(x, y) = In(25 – x² – y²). %3D а. Find and sketch the domain for this…

A: Given function   f(x,y)=ln25-x2-y2

Q: Question 1 Let f (x) = Vr, a > 0. Prove using e - 8 methods that f is continuous at every point of…

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Q: Given a surjective function f: [-1, 1] → [-1, 1], prove or disprove: f-(f{}) = {0}. Find f(E) and…

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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: 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: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: let a function f(x) be given by f(x) = log(r +x) prove that f log(e+x) (x)is decreasing on [0,0]| ]

A: The solution for the above question is as shown below.

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: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: ich of the following functions have at least [x)=-x+ (x) = x ƒ0=(1) f(x)= log₂x f(x) = cos x a) ii…

A: Topic:- calculus

Q: 3. If G(x) = tan x, find G(rt/6), G(x - T/2), G(-x) and express G(2x) as function of G(x). 4. If…

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Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

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

A: Solution

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: If ø(x) =(x)+ f(1-x) and f"(x)<0 for all x e increasing in [0,1/2] and decreasing in (1/2,1].…

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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.

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Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

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: (a) Show that z = 0 is the unique branch point of f(z) = log(z)

A: Since you have posted a multiple question ,I will solve the first question (i.e(a))  for you. To get…

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: 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.