Find the following limits if they exist. 1. 2 8x 4x+1 lim x0 x-7 2 lim x0 5x-7 X +2 x +x+ 27 lim 2 X+0 X- 4 3.

Q: 2. y" + 2y' + y = 8(t – 1) + e2t y(0) = 0, y'(0) = 0

A: Given differential equation is y'' + 2y' + y = δ(t-1) + e2t  with   y0 = 0  and  y'0 = 0

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A: Given differential equation, x''+3x'+4x = 2sin(2t)

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Q: (b) Show that 1 11 2 k(k + 2)(k + 4) 96 k=1

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Q: B. Determine if the following mappings are linear transformations. Explain your answer.

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Q: (x*dx-xydy), wher hond

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

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Q: Decide whether the argument is valid or a fallacy, and give the form that applies. If she likes chee...

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Q: Q7 Let A = [(p → q) ^(~p → ~q)]. Construct a truth table for A and determine if it is a tautology, c...

A: p q [(p→q)∧(~p↔~q)] 0 0 1 0 1 0 1 0 0 1 1 1 [(p→q)∧(~p↔~q)]p⇒q=q∨~p~p⇔~q=(p∧q)∨(~p∧~q)(~p...

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Q: 54. If sz is the k th partial sum of the harmonic series, prove that In (k + 1) < S <1+ln k. Hint: 1...

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Q: offered cooking classes 24 of the 30 days in November. What decimal is equivalent to the fraction of...

A: Introduction: The division is a basic arithmetic operation in which a larger number is divided into ...

Q: (c) Are the vectors v1 = (3,1,2, 1), i2 = (-1,0,1,0), iz = (3,0,0,3), T4 = (5, –2,0, 4) linearly ind...

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Q: Which is NOT a solution of V2 - i ? C. -0.4717 + 1.2196i D. -0.8204 - 1.0183i A. 2.2094 – 0.3442i B....

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Q: Overall Costs of Goods. An operation’s beginning inventory on October 1st was valued at $54,000. Pu...

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Q: Parametrize the following two curves in R³ and find their arclength. (1) the intersection of the cyl...

A: Question 1:Given:The intersection of the cylinder x2 + y2 =1 and the plane x+y+z = 1  

Q: |a² + 1 ab ac The value of the determinant A= ba b2 + 1 bc equals cb c2 + 1 са A. a? + b? + c? B. 1 ...

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Q: Solve. 6.) A plane flies 403 miles from Springfield to Rochelle with a bearing of N22 E. Then it fli...

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Q: Prove the above property. That is, prove that if a mod n = k and b mod n = j, then (a + b) mod n = (...

A: If a mod n =k and b mod n=j show that a+b mod n =j+k mod n. Definition: If x mod y=z, then y | x-z. ...

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Q: A sequence is defined recursively by a1 = 9, a2 = 99, and An = 11ап-1 — 10аm-2 for n > 3. Use strong...

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Q: Q.5// Solve games matrix by arithmetic method: 549 95 95 4 4 5 4 9591 4.

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Q: 3. Suppose that r(t) < s(t) on [1, ), and r(t) is continuous and strictly decreasing on [1, 0). If S...

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Q: Show that [~q a (p → q)] →►p is tautology by constructing truth table.

A:   We know that A tautology is a compound statement in Maths which always results in Truth value. and...

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Q: function with form y = ax

A: Given,  A power function y=axp passes through the points 3,781 and 6,71296. The equation of power fu...

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Q: Find a basis for and the dimension of the solution space to the following homogeneous system of equa...

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Q: 3. Let {an} be a sequence of real number. Suppose that the power series on R below > an(x – a)" n=0 ...

A: Given that an be a sequence of real number. Suppose that the power series ∑n=0∞anx-an is converges a...

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Q: If x is equal to the square root of (-7+ 24i). Solve the principal root of x. C. 3 + 4i A. 3 + 3i B....

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Q: Evaluate the integral of the two-form w = 3xe 3zy d A dy over the region D= {(x, y) E R² | x € [1, 5...

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Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary ex...

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Q: Find the Inverse Laplace Transform of the following: 2. Y(s) = /(2s– 3)5

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Q: Q1. Let U = {x: x e Z, 3 < x < 15} be the universal set, A = {x: x e U and 2 < x – 3 < 6}, %3D %3D B...

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Q: Determine the principal value of log; 2i A. 1- 0.441i C. 1- 3.02i B. 0.198 – 0.134i D. 1 - 1.73i

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Q: nink about Write the Correct Comparison Symbol (>, < or ) in Each Box 1 ) 11) 10 2) 12) 능능 13) 4) 14...

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Q: Find the general solution of a given non exact DE y(8x-9y)dx+2x(x-3y)dy=D0. (Note: Express your answ...

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Q: If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum...

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