Q-3: a) For all integers a, b, c, d, determine whether each of the following is TRUE or FALSE, Justify your answer: 1. If alc and blc, then (ab)|c². ii. If alb and cld, then (ac)|(b + d). iii. If ab, blc and c|d, then ald. iv. If alb and cld, then (a + c)|(b + d).

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Q: (1) Let A={1,{2},{1,{2}}} (a)True or false: 2 € A, {2} € A, {{2}}CA, {1,2}CA, 3x(x € A^xA)

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Q: 9) Solve the equations by Cramer's rule: 2x-y + 3z=-3 3x+3y-z=() -x-y+z=-4

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Q: 3. Consider the function gx=lnx-16) a) Find the input values on the graph of g x out values for g(x)…

A: Introduction: A function's domain and range are its constituent parts. A function's range is its…

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Q: 3. b. TE Evaluate using Beta Function: sin³ 0 cos 0 de

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Q: 9. 10. |C/G|| y" + 3y' + 2y = 1 + d(t − 1), y" + 2y' + y = et +28(t− 2), y(0) = −1, y'(0) = 2…

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Q: The system of first order differential equations: y/2 = = 3 y₁ + 2y2, -34 yı 13 y2, - 3₁ (0) = 4 32…

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Q: In an integro-differential equation, the unknown dependent variable y appears within an integral,…

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Q: (ii) If f is continuous at xo, prove that F is differentiable at xo, and F'(xo) f(xo).

A: f:a,b→ℝis Reimann integrable . Fx=∫axftdt f is continuous at x0 f bounded

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Q: Find the area bounded by the curve and the line y = 13. Area = x = t-1/t y = t+1/t

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Q: dr (linear differential equation) Solve:- de +rsec 0 = cos 0.

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Q: 6. Use an appropriate test, and clearly indicate which test you are using, in order convergence or…

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Q: 1. Let fE LP(R). Consider the operator T defined by 1 (Tf)(x) = So x f(t)dt Show that the operator T…

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A: The given function Hx=∫-xxeu2du. We have to find the value of H'0.

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Q: 1. If f(x) = x² + 1 and g(x) = (x + 3)" determine domain and range of following functions F'(x)) =…

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Q: 8. Use strong induction to prove that any amount of 10 cents or more can be formed using only 3-cent…

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Q: 2 5) Let z=xsin (y) əz Compute & as əz ət x=s².t y = st. in two ways: (i) Using the chain rule and…

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Q: Eliminate the parameter t to find a Cartesian equation for: B where A = and B = and C= x = 1² y=6+3t…

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Q: Find the gradient vector field (F(x, y, z)) of ƒ(x, y, z) = x³y³ z z F(x, y, z) =

A: Solution :-      The given function is     f(x,y,z) =  x6y3z4   then , we have to find gradient…

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Q: 0 ccab(ar) Dzah(x) || 2.000(x4/2)

A: The given problem is prove the following definite integral using method of complex variables.