Given Function f:R→R ² sin (1x). {+² 0, f(x)= with if x #0 if x=0 Prove That f differentiated on R.

Q: Example 2: The population of a village in 12 people can be modeled with respect to time in t years…

A: We have to find a) Population of the village in b) Projected average growth rate of the town between…

Q: For example H = {he Z10 ne Z} = {02468 is the set of even numbers in modulo 10 includes addition and…

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Q: Let the supply and demand equations Qd = 9-P +P′+P′+3P′′ and Qs = -1+4P -P′+5P′′ with P(0) = 4 P′(0)…

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Q: 2. y" +9y = 2x+1, y(0) = 0, y'(0) = 1

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Q: 2. Let m, d N and assume that d | m. Prove that if a = a + mZ is a square in Z/mZ, then a' = a + dZ…

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Q: Use the Principle of Mathematical Induction (PMI) to prove the following for all natural numbers n.…

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Q: Consider the function f(x) = − ½ (2−²)(2³) — 1. Determine the exact value of the y-intercept of the…

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Q: et W be a subspace spanned by the u's​, and write y as the sum of a vector in W and a vector…

A: Orthogonal Projection of y onto span  is

Q: Use the Principle of Mathematical Induction (PMI) to prove the following for all natural numbers n.…

A: We  have to  prove  that for  all  natural number n (using  induction  on n.)For we  have  Thus,…

Q: Problem 11 Find the number of elements in A₁ U A₂ U A3 if there are 100 elements in each set and i…

A: We have three sets   and   , each containing 100 elements. Let's find the number of elements in the…

Q: Human blood can contain the A antigen, the B antigen, both the A and B antigens, or neither antigen.…

A: The given samples and the antigen in the blood.# of samplesAntigen in Blood1893013211186AA and BBB…

Q: Utt = c²uxx u(0, t) = 0 u(x,0) = ax, 0 0 t> 0

A: Given: Objective: To solve the vibrating string of length  with ends fixed at and free at…

Q: (1). Write a computer program using MatLab that finds the zeros of a function f(x) using the secant…

A: Given:The function Two initial guesses for the root:  and The error tolerance is set to…

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Q: Obtain the solution of the SDE dX₁ • (-/-X₁) dt + √XidW₁. Xo = 220.

A: Given SDE(stochastic differential equation): Objective: The objective is to find the solution  to…

Q: Find the inverse Laplace transform L¯¹{F(s)} of the function L-¹{F(s)} F(s) = = = NOTE: The answer…

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Q: Given groups (R+, ) and (R, +). Show that maping ƒ: (R, +) → (R+,-) ex X Vx E (R, +) is an…

A: Given  that   and   are  groups.Let  be  defined  by  1) is  well-defined  and  onre-to-one: Thus, f…

Q: Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3,…

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Q: Problem 5 A coin is biased so that the probability a head comes up when it is flipped is 0.6. What…

A: A coin is biased so that the probability a head comes up when it is flipped is 0.6. What is the…

Q: 2. The region of experimentation for three factors are time (40 ≤ ≤80 min), temperature (200 ≤T₂…

A: Given: The model is .The region of experimentation for three factors are time (), temperature (),…

Q: Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,1), (1,2), (1,4), (2,2),…

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Q: A population of rabbits live in a meadow. The population began as only 10 rabbits, but their growth…

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Q: Exercise I.1. Consider F := B := {v € R" : ||v|| ≤ 1} and fix xo € R". (a) Suppose to, t₁> 0 and vo,…

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Q: 2. Suppose that the odd, 2-periodic function f(x) has the Fourier series expansion 1 1+n³ (A) g(x) =…

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Q: Find all global minimum points of ƒ in R³, if ƒ (x1, x2, x3) = ex² + x½ + 2x²x3 + x² − 8x2 - 8x3

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Q: Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and…

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Q: Question 5. Apply the definition and prove that the set A = { } } } } denumerable. } is

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Q: (a) Using the decision variables x4 and s4, write a constraint that limits next week's production of…

A: As per the question, we are asked to model the production planning for a manufacturing company that…

Q: Pivot once as indicated in the given simplex tableau. Read the solution from the result. Pivot…

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Q: Check if ¬P is a logical consequence of:

A: To check if is a logical consequence of the given premises, we need to determine if the premises…

Q: Question 3. (a) Let f: R→ R, f(x) = 2³+1. Is this function onto its indicated codomain? Prove your…

A: Q.3 (a) Let , . Is this function onto its indicated codomain?Prove the answer.(b) Let , . Is this…

Q: Problem 10 A survey of households in the United States reveals that 96% have at least one television…

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Q: are you

A: The solved answer is (43/60).

Q: Doris is an entrepreneur who purchases from wholesale suppliers and resells these items to her…

A: To determine the optimal order quantity and the feasible range, we need to consider the cost…

Q: Exactly one of the following sequents is invalid. Use whatever method you wish to determine which,…

A: The objective is to determine which of the two sequents,  or , is invalid.

Q: a direction field for d = 2t+y². Use the direction field to sketch a solution cu on y(0) = -1.

A: To draw the direction field of the DE , let first find the equilibrium points.(There is a misprint…

Q: 1. y" + 5y + 4y = 5e4x + 4, y(0) = 0, y'(0)|= 1

A: The differential equation is .We have to solve the given differential equation.Note: According to…

Q: Problem 2 Suppose that we flip a fair coin until either it comes up tails twice or we have flipped…

A: Suppose that we flip a fair coin until either it comes up tails twice or we have flipped it six…

Q: Find the minimum and maximum values of the function f(x, y, z) = x - y - zº subject to the…

A: To  find the  minimum and maximum values of the function subject  to the constraint .Differentiate…

Q: (a) A = 1 -1 02 18 8 0 3 1+ i 1 6

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Q: 1. Find the domain of the vector function. a) r(t) =(√4-t², e-³t, ln(t+1)) t-2 b) f(t) = i+tan…

A: We have to find the domain of the vector function.

Q: Problem #1: (a) Consider the Laplace equation શક Oy² = 0, x² +1² <1, (1) with the boundary condition…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: We have to find the local maximum and minimum value and saddle point(s) of the functionf(x,y) = 7ex…

Q: x - 5y Find √√√₁ -dA, where R is the parallelogram enclosed by the lines R −6x + 6y 6x + 6y = 1,…

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Q: [5] [General Richardson extrapolation] As mentioned in lecture, Richardson extrapolation is a very…

A: Given: Objective: Find constants  and  such that , where the error term is of the form

Q: 2 Let y = 6. u₁ T 11 I W|N w|→ 3 WIN 2 3 II 2 W|N 2/3 113 and W = Span {u₁,u₂}. Complete parts (a)…

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Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: To find the extreme values of the function  subject to the constraint  we can use the method of…

Q: Given a rectangular wave below, obtain the value of the coefficient of the 9th harmonic of its…

A: We obtain the value of the coefficient of the 9th harmonic of its Fourier series, if A = 6, and…

Q: 1, The function f(x) = x³ was transformed through a series of transformations. The resulting…

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