1. Given f(x)=2x+5 and g(x)=(x-5), (a) Determine (i) f(g(x)) (b) What is the relation between f(x) and g(x) ? (ii) g(f(x))

Q: 1 (-1)-1 (ii) 1 +... 5 2n-1 (b) Show that the interval of convergence of the series 1 1 -√2ses.…

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Q: Question 2: Determine the nature and stability of the equilibrium points of the system dz = z-y+z²,…

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Q: (2) Explain why the rational numbers are those having periodic representation or with- out infinite…

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Q: Linear Algebra Question: Suppose x1, x2, x3 are 3-tuples in R^3 satisfying the following: a. x1 is…

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Q: Suppose the function f: R → R has Fourier transform f(p) = 1 1+ 4π²p² бетра i. What is the Fourier…

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Q: CORRELATION ANALYSIS Determine the relationship between the number of hours students spent per week…

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Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

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Q: Use the trapezoidal rule with five intervals to evaluate the integral i √√√-1da, correct to four…

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Q: 23. A population grows according to the logistic growth model, with growth parameter r = 0.8.…

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Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

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Q: Question 6 Option 1 Two cars leave an intersection at the same time, each on a different straight…

A: Here we have to use cosine rule for triangle  For a ∆ABC cos A =b2+c2-a22bc where a,b,c are sides…

Q: Show that if b0 = 0, then (g^xm)≡ 1 (mod p). Q2: Show that if b0 = 1, then (g^xm) ≡ p − 1 (mod p).

A: Given: x is a number in the set {0, 1, . . . , 2t} x written as: x = b0 · 20 + b1 · 21 + b2 · 22 + ·…

Q: Evaluate the integral sin(x²)dxdy.

A: This is a question from the double integral.

Q: Let FCK be fields, and let u # 0 in K be algebraic over F. If ceF, then cu is algebraic over F. O…

A: We have to check whether the following statement is true or not : Statement : Let F⊆ K be fields and…

Q: (D² -1)y=2(1-e-2x)-1/2

A: Solution: Given a differential equation D2-1y=21-e-2x-12 Now, the characteristic auxiliary equation…

Q: X If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

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Q: Question Three Let f(x) be a function given by 0 f(x) = { sin (a) Prove whether f(x) is a Dirichlet…

A: Given: Let us consider the given function, fx=0-π≤x<0sinx0≤x≤π a) Let's show the given fx is a…

Q: The value of B in the equation 3x+9y=1

A: Given: 3x+9y=1 To find: Value of b in given equation.

Q: Q1. Test for conditionally converge, Absolutely converge, or diverge of the series Σ+(-1)n Inn

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Q: 4. In Chebyshev polynomials form, the value cos 20: = ...

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Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 49 The solution is - 2√/y = In (x-9)-…

A: The given initial value problem is                                      ydx+(x-9)dy=0, y(10)=49 We…

Q: Pick any two nonzero numbers. Add them to obtain a third number. Construct a sequence of numbers in…

A: We have to examine the nature of Fibonacci sequence by taking any two non zero numbers and adding…

Q: 3) By changing the independent variables x and y to u and v by means of the relations u xay, v = x +…

A: Apply chain rule

Q: The equation of a function is y = 4x + 3. A second function contains the table of values below. X y…

A: Given that the first function is y=4x+3 and the second function contains the following table of…

Q: How much should be placed in a fund every 3 months in order to have Php350,000 in 4 years if the…

A: The formula for future value of an annuity is defined as, F.V. of Annuity=P1+in-1i where, P=Periodic…

Q: (b) Let g(x)=√x with domain {x|x ≥ 0}, and let > 0 be given. For each c> 0, show that there exists a…

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Q: Problem: A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50,…

A: We have to find the number of acres of wheat and barley to maximize the farmer's profit.

Q: Write the first four terms of the sequence: an = 3n + 4 . If a1 = 2 and a3 = 8 of an arithmetic…

A: We have to write the first four terms of the given sequence. Then, we can proceed further.

Q: Question One (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x1 for 2 ≤ x ≤ 3. 1 Prove…

A: Solution : a) f(x)=x2-3x+12x-1 2≤x≤3 f(x) is a rational function and bounded because its pole x=12…

Q: 3.) Evaluate ff cos(x-y) sin(x+y)dA, where R is the triangle with R vertices (0,0), (-л,π), and (,)…

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Q: Determine for which values of m the function (x)=x" is a solution to the given equation. 2d²y dy (a)…

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Q: 9. Prove that if G is a group of order 60 with no non-trivial normal subgroups, then G has no…

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Q: 2. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = x²…

A: Given curve is y=x2, x=1 and x=2. We have of find the volume of the solid obtained by rotating about…

Q: Use the trapezoidal rule with five intervals to evaluate the integral 2 Type your final answer below…

A: The given function is fx=1x2-6x+10 To find: ∫23fxdx by trapezoidal rule.

Q: Assume g(x,y) is a function of the form x³y g(x,y) = √²x²y³² ( O 1g (x, y)| ≤ lally! then < Show…

A: Solution ; g(x,y)=x3yx2+y2,(x,y)≠(0,0)0,(x,y)=(0,0) Use parametrization to prove required result,…

Q: a) How many binary relations exist on an empty set

A: To find: number of binary relation on given set. Please post the multiple questions separately. Here…

Q: Consider this scalar-valued function: f(x,y)=y/ 2x^2+y^2 . After, find the gradient of f and find…

A: First, we have to find the gradient of the function f. Then, we can proceed further.

Q: (a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the…

A: As per our guidelines we are supposed to answer only one question. Here first question answered.

Q: There is a function with two variables f(x,y)=exy + √x +2 (i) Find the first order Taylor…

A: As per the question w are given a bivariate function as : f(x,y) = exy + √(x+2) And we have to find…

Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 49 The solution is (Type an implicit…

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Q: Let T:P2 →M be defined by T(p(t))=[p(1) p(1) p(1) p(1) p(1) p(1)], where P2 ={at2 +bt+c,where a,b…

A: We will use Sylvester law for finding dimension of range of T.

Q: Number of voters 10 16 1st choice C B D 2nd choice B A B 3rd choice D C A 4th choice A D C Find…

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Q: The average speed f(t) (measured in kph) of traffic in a certain municipality between 4 PM to 8 PM…

A: It is given that the average speed of traffic is approximated by the function ft=20t-40t+50. We have…

Q: Evaluate the following limits: sin(4x-8) 4. limx→² 4x² −5x-6

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Q: Assume that g(x, y) is a function of the form x² + y² g(x, y) = 0 (i) Show that if (x, y) = (0,0),…

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Q: 2) Perform the following index shifts: i. Write y = no anx" as a series that starts at n = 2 ii.…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: a. b. C. (x+y) dx+(x-y)dy = 0 (2xy − 3x² ) dx + (x² + y)dy = 0 (2xy + y) dx + (x² − x) dy=0

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Q: •4.0.5 f Determine area the top and all side of a platform below. Note// Parallogram shape 6m -2.65m…

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Q: Jse chain rule to differentiate the following 1 y = sec+ (√x+; )

A: Differentiating given function below

Q: Determine area the top and all side of a platform below. 6m -2.65m 115°

A: Consider the diagram below, The height of the parallelogram will be find by using trigonometric…