Let V be the vector space of functions from R into R. Show that f,g,h EV are independent where: f(x) = e2x, g(x) = x² and h(x) = x

Q: 5. Let T: R R3 be defined by -> X1 + 2x2 X1 T %3D a. Find the matrix [T]B.B relative to the bases B…

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Q: What is the region of the solid generated by the graphs of a = y – 4y and a = -y ?

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Q: find the total dominating set for: Kmin

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Q: 2. Determine the volume generated about y-4 the area boun ded bay ×キの x and x?ty =3 メ %3D

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Q: B. Solve the following problems using differen linear approximations. Show complete soluti 2.…

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Q: QI/ Find L{sin(at + b)} 3 Q2/ Find L-1{-}, by completing square. s2+

A: To find: (1) L{sin(at+b)}(2) L-1{3s2+s4}

Q: 1. What theorem states that the square of the hypoteuse of a right triangle is equal to the sum of…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 5. Let T: R2 R be defined by [x1 +2x2 T a. Find the matrix [T]B.B relative to the bases B = {u,, u}…

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Q: What sum of money must be deposited at the end of every three months into an account paying 3.7%…

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Q: u, = and u, = Find (T]B- Verify that Formula (8) holds for every vector x in R2.

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. - 12n…

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Q: 5. Fill in the blank: For x, y E R. Equality in the Triangle inequality is satisfied, i.e. |x+y| =…

A: Let us consider x,y be any real number  then  Inequality Resultant xy>0 x>0 and y>0…

Q: L3x3 + M (subspace sum). sym 3×3 !! L3x3 O M (direct sum). sym 3×3 !! express A E M3x3 as A = L+U…

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Q: Don borrows P5000 for 2 years at 4% per annum simple interest. He imrnediately lends it to another…

A: Explanation for the correct choice. The formula for the simple interest is I=PRT100. Initially,…

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

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Q: s (x) In (1t x2) 74.8

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

A: We have to find the maximum and minimum value of the given function.

Q: Set up and simplify (but do not evaluate)/ F. dr, where F(x,y) (x2, xy), andC is the arc of the…

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Q: 21 o (z) = of the nth mode is cos for all n n² for odd n and 0 for even n n² for even n and 0 for…

A: Sol

Q: he curve y = X fc (vî (yi

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Q: 2. What can you infer from the axioms and illustrations of the three-line and four-line geometries

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Q: Find the partial derivative of the function g(r,0) =r cos 0 +r sin 0.

A: We have to find the partial derivative of the function.

Q: What is the 109th term of the arithmetic sequence (963, 936, 909, 882, ..)?

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Q: Draw the graph of the function. Draw the contour plot of the function. Point out the local ex- creme…

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Q: Find the area of the shaded region. The image is not to scal y = y= Consider c=64. Enter the exact…

A: Area bounded by the region

Q: f(2.3) of the following table by using Finite differences is 1 3 4 5 y 3 34 115 270 523 53.8580 a…

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Q: 4. Apply to the initial value problem y' = -ry + 1, y(0) = 0 three steps of the Picard-Lindelöf…

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Q: Let P. Q. R be true, false true, respectively. Which of the following is true? * PA ΡAQAR PA~Q ^~R O…

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Q: Find the inverse Laplace transform of s+1 F(s) = e-2s, %3D s2-2s + 2

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Q: |Example 6.12. Prove with the usual notations, that (i) hD = log (1 + A) = - log (1- V) = siiih- (E)…

A: Please find step by step solution below:

Q: Consider the polar curves C2:r=4 cos e and C3 :r = 4 sin 0. (a) Determine the slope of the tangent…

A: We will find point of intersection. Derive slope of tangent for.polar curve and then substitute…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x3/2 from (0, 0) to (4, 8)

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Q: Use an appropriate test to determine whether the series given below converges or diverges. (In n) Σ…

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Q: Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros…

A: The given polynomial is ex=8x8+7x7+6x6+5x5+4x4+3x3+4x4+3x3+2x2+x

Q: 4. Find a general solution of the linear system. x' = 2x + y = x + 2y – e2t

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Q: IExample 6.9. One entry in the following table is incorrect and y is a cubic polynomial in x. Use…

A: The problem can be solved by making difference table.

Q: 10. All are equivalent but which among the following versions was due to Archimedes as recalled in…

A: We have to show that there is a statement which is equivalent to Archimedian property.

Q: what is the fuzzy power set ? And give examples

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Q: Show that the following method is convergent, and determine it's global order of accuracy. 1 At (Yn…

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Q: aw- Let Z[/2] = {a +b/2 |a, b e Z} and let H = { b а 2b : a,b eZ }. a Show that Z[ /2] and H are…

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Q: Example 3.37. Solve the equations 2x2 + 3xy + y? = 3, 4x² + 2xy +y = 30 correct to three decimal…

A: Here, We need to use the newton-raphson method. x0 = -3 y0 = 2

Q: Hw.1. Solve the integral equation g(s) = f(s) + a S,(s + t) g(t)dt

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Q: Torontiating torm-by-torm givos 02 sin 0<r< L. n odd o weaker series convergence is casily n. and it…

A: Sol

Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

Q: Find Taylor series of the function: f(x) = V9 – x2 1.

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Q: 3. Let C1 be the circle r = 3 cos 0 and C2 the cardioid r = 1+ cos 0. %3D (a) Find all point(s) of…

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Q: What is the transitive closure of the following graph? a

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: (a) Consider the real linear map T : R' - R', expressed as follows: (1 2 -1 49 -1 X1 X1 + 2x2 - x3…

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Q: 3- 2i 2 + 3i 1-i II. E = P = 5 4 + i -i 1+ i

A: Sol