(a)x - x = 2t x(0) = 1 x(0)/ = -2

Q: 3a N(x) Va (N(a) 1(æ)) .. Bar I(a) Statement Reason ..... ........... ............ .... .......…

A: Modus ponens says that: ∀x if Px then Qx∃ x Px∴∃ x Qx This argument is valid.

Q: d) U(B, :ieZ)

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A: (a) 5 members can be chosen from 11 members in C511 ways. C511=11!5!×6!=462

Q: Example:4 Verify Cayley-Hamilton theorem. Hence find 2 -1 A-1, A -1 2 -1 1 -1 2

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Q: 7. Simplify using Set Identities. Indicate the rule applied for each step. (AN B)U (C nĀ)NB…

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Q: Find the inverse Laplace transform following: 0.2s+1.8 1. s+3.24

A: The problem looks difficult with decimal point but it isn't. Note that 3.24 = (1.8)^2 and so the…

Q: Number 2

A: To Evaluate: cos2(2-i)

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A: A solution is something when we plug in the values of x we both the LHS and RHS become equal. That…

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A: Follow the steps.

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A: a. To compute 71529 mod 51. As per Fermat's Little theorem ap-1≡1 mod p if a and p are relatively…

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A: Volume bounded by the xy-plane

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Q: Name and sketch the graph of y² = z in R³.

A: To Sketch: y2=z  in ℝ3.

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Q: I Example 2.16. Using the bisection method, find an approximate root of the equation sin x = 1/x,…

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Q: Determine the Inverse Laplace Transform of the following: 4 3 1. + 52+4s+4 + s2+2s+2

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Q: 200 Ei. Calculate the sum j = 1

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Q: 1. Find the solution of the systems of linear equations by Gaussian elimination using the Maximum…

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Q: tw.t Find the Volumes for the fallowing solids heishts are defined by ZCX,y) and bases are the…

A: Volume bounded xy-plane

Q: Vaæ (L(a) F(æ)) 3a (L(a) AC(æ)) . Ba (F(a) A¬C(x)) Statement Reason ...... ........

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Q: 2 Evaluate V4-x? Jo J2- dy dx using polar V 2x-x2 Coordinates.

A: Solution:-

Q: 5. Suppose that f(n) satisfies the equation f(m+n) = f(m) + f(n) – 2f(mn) for all integer m,n >0,…

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Q: 200 ? Σ21-Σ2(i + 1) , %3D What is the upper limit of the sum on the right ? i = 1 i =0

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Q: I = 10+ 2s I - 1 y +3 12 - z Consider the lines defined by the equations l1 : and l2 : 9. y = 5s 7 z…

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Q: Calculate the Laplace inverse of 4s +8s 10. F(s) = (s- 2)(s² – 4s +13)²

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Q: [a, b If A, = |d, e, fil [az bz c Az = |d2 ez fal [az b, cs] Az = [d3 es fsl and are any 2 x 3…

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Q: Let G be a solid shape enclosed by a surface x*2+ y*2 = 1, z = 0 and z = x*2+ y*2+ 1. 1) Draw the…

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Q: -a) Complete the table below for the given equation. b) Graph the equation using STEP Methor or Two…

A: In the given question, the concept of the parabola is applied. Parabola A parabola is a curve…

Q: * - x(t) + 5ÿ(t) = t; ÿ – 4y(t) – 2x(t) = -2; y(0) = ÿ(0) = x(0) = ¿(0) = 0 %3D %3D

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Q: For y= sintx/2 obtain dy/dx at x= 0.5 with Ax= 0.1 using: dy。+1-リ-1 (a) dx 24x dy Yj+1-Y;. (b) dx 4x…

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Q: Integrate the fallswing funtinnaaver the given ke R: y24X-x? and yex-

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Q: Differentiaaliyhtälöpari Sa'(t) = -a(t) + y(t) lo (t) = i,#(t) – y(t) kuvaa kahden symbioosissa…

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A: a. It is not a power function.

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A: Volume bounded by the xy-plane

Q: The Maclaurin series expansion of tan- is given by tanr = Σ +1 for z € (-1, 1). (2n + 1) n=0 (4) Use…

A: Given below clear explanation