Consider f and g in V = C[0,1], with the inner product (f.g) given by the integral [f(t)g(t) dt. 0 Compute ||f||, where f(t) = -5+15t². fl=

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A: For first part consider an example which is following :Here  has no solution, but  has many least…

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Q: For what value of m, the vector (m,3,1) a linear combination of e1=(3,2,1) and e2=(2,1,0)  ?

A: The vector  is a linear combination of  and .We have to find the value of .

Q: Find a vector that is orthogonal to each of the three vectors below: V1 4 V2 0 and V3 = 1 3 3

A: A vector orthogonal to  is (Gram-Schmidt Process)

Q: Solve the following equations using matlab. 1. 2.) z¹+(5-14i)z²-(24+10i)=0

A: Given equation: Objective: To solve the equation and find the roots using MATLAB.

Q: Use the Intermediate Value Theorem to show that the equation sin (7) -ecos (72) = has a solution in…

A: If there is a real number k such that f(a) <=k<=f(b), then the intermediate value theorem…

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Q: . If A and B are sets in a universal set U, then AUB=AnB. A-(BnC)=(A-B)U(A-C). . If A, B and C are…

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Q: 1) Use the definition to calculate the Laplace transform of the following functions. a) eat…

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Q: (a) (b) Verify whether the vector X = equation dx dt dy dt = 10x - 5y =8x-12y 7643 14 -10/ е X'= is…

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Q: Describe something that is changing over time that can be modeled using a logarithmic function.

A: We have to describe something that is changing over time that can be modeled using a logarithmic…

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Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini For Legendre's…

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Q: 7.2.17 Show that To Ta dx (x² + a²)² = Л 4a³' a> 0.

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Q: Let K be an extension of a field F and let a∈K  be an algebraic element of degree n, then [F(a):F]=n

A: Let K be an extension of a field F and let be an algebraic element of degree n, then we have to…

Q: Fourier transform can be employed among which of the following? pulse functions O exponential decay…

A: The Fourier transform is a mathematical formula that transforms a signal sampled in time or space to…

Q: Prove that the linear sum of two subspaces of a vector space is also a subspace

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Q: Find the general solution of the given higher-order differential equation. y"" + 3y" - 16y' - 48y =…

A: The given differential equation is .We have to find the general solution to the differential…

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

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Q: ical coordinate limits for the integral that calculates the volume of the solid enclosed by the…

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Q: The price-demand equation and the cost function for the production of table saws are given,…

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Q: Is the set of all polynomials p(t) in P, such that p(0) = 1 a subspace of Pn for all integers n ≥ 0.…

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Q: 6. Suppose A, B and C are sets. Prove that if AB, then A-C≤B-C.

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Q: RACTIONS Subtraction of mixed numbers with different denom Subtract. Write your answer as a mixed…

A: Given mixed fraction number We have to find the subtraction.

Q: Find the area of the parallelogram whose vertices are (0, -2 (5,-2), (-3,1), and (2, 1).

A: Introduction: A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite…

Q: (b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close…

A: note :As per the instructions we will only solve part (b) of the question.

Q: Find the number of distinguishable arrangements Of the letters of the Word Sex Decillion There are…

A: In the word of "Sex Decillion", there are 12 letters in it.But these letters e,i,l repeated 2…

Q: 81 -1 d.x 3√x arctanx dx

A: An integral converges if it has finite value and diverges otherwise.

Q: 5. An integer a is odd if and only if a³ is odd.

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Q: Number of culère equation of intequal 2n's NO

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Q: Consider the following. (If an answer does not exist, enter DNE.) C(x) = x¹/(x + 8) (a) Find the…

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Q: Prove that {9":ne Q} = {3":neQ}.

A: Two sets A and B are equal i.e. A=B if and only if

Q: Solve the following equations using matlab. 1. z²-(8-5i)z+40-2i=0

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Q: 2. Suppose x € Z. Then x is odd if and only if 3x + 6 is odd. 3 Given a integer ther 3 if and nly…

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Q: Solve the given differential equation by undetermined coefficients. y""y" - 16y' + 16y = 6 - e* + ex…

A: The  given differential equation is,homogenous equation becomes,

Q: Find the volume of the parallelepiped with one vertex at the point (-1,-1,-1) and adjacent vertices…

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Q: Use the Gram-Schmidt process to determine an orthonormal basis for R3 starting with the following…

A: Use the Gram-Schmidt process to determine an orthonormal basis for  starting with the following sets…

Q: en's Theorem to evaluate the integral. C (By dx + 5y dy) The boundary of 0≤x≤, 0 ≤ y ≤sin x A) -6 B)…

A: We have to apply the Green 's theorem to solve the given problem.

Q: Determine where the function f below is discontinuous: √x+10 if x7. A. At x=7 only B. At x=0 only C.…

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Q: Let FMN be the transformation of the surface. Prove F*dg=d (F*g) gEA (N) = S(N). where

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Q: 6. Prove the result in Example 10. Use the fact that if xy = 0, then x = 0 or y = 0.

A: Given:A list of distinct primes .Objective:To prove this above by using the fact that if then  or .

Q: 1.2p 2.3q3.1r + 10.1 = 0 - 5.3r — 21.5 = 0 + 7.4r + 28.1 = 0 +.7p+3.8q 3.7p8.3q

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Q: Find the area inside the curve defined by r = 2 + cos (0). T 3 T 4 5 π 4 E|N D 3 R 2 Enter the exact…

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Q: In 2022, a new ALZA car is purchased for RM65,000. During the next 10 years the rate of change in…

A: The purchase price of the car is The value of the car is modeled by the differential equation Note:…

Q: Problem 6 Given the two vectors u and v in R" the Cosine of the angle 0 between them is defined as…

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Q: power W 1 2 3 4 Y 5.6569 6.9282 . 4 5 8.944) 6 9.7980 Find the equation of the function of the…

A: Here in the given question, there are 6 observation and the values of x and y are increasing with…

Q: Let A = True False -8-2-9 4 0 6 4 Is it true that w is in Col(A)? 8 4 and w H

A: Let  and .Is it true that  is in  ?1. True2. False

Q: Recall that with​ base-ten blocks: 1 long=10 ​units, 1 flat=10 ​longs, and 1 block=10 flats. What is…

A: a) 20 long pitches in base six:We have six numbers in base 6 (0, 1, 2, 3, 4, 5) We must determine…

Q: Find a description of the following curve that uses arc length as a parameter. r(t) = (6 + 4t)i-3tj,…

A: curve is,