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Q: 1. If f(x) = ax² +b where a and bare real constants, then show that (a) f[xx] = a (x₁+x). (b)…

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Q: Select the correct classification for the given 1st order ODE: dy + 2xy = y³ O linear, not separable…

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Q: dy xy+3x-y-3 dx xy-2x+4y-8 - - In (²+4) ³ = Ans: y-x + In y+3, = C

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Q: 28. Consider the autonomous equation dy/dt ferentiable, and suppose we know that f(-1) = f(2)= 0. =…

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Q: Consider the boundary value problem: x²y''(x) + xy'(x) − (x² + 2.89) y(x) = 0 where y(0) = 0 and…

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Q: Let C :Let (F. +..) is a field and f(x) E F(X). prove that f(x) is irreducible polynomial iff the…

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Q: 3. Derive the following Newton-Cotes formula. 1 (a) f f(x) dx ≈ A₂. = AS (-=-1) + AS ( 1 ) Af -1 2…

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Q: B: use Lagrange interpolation formula to determine the relationship between the force and velocity…

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Q: 3. Prove that every connected subset of R is an interval.

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Q: What is AUB? U =R A = {a E Na is a multiple of 3 less than 15} B={beZ-15 4} 4

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Q: The displacement of a particle is given by s-4t-66t2 +113t-41 wheres is in feet and t is in seconds.…

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Q: 1. Eliminate the arbitrary constant. y² = 4C(x + C) 2. Obtain the general solution. (Let 2C=C) (4x +…

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Q: Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and…

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Q: What are the horizontal asymptotes of the function in the figure? 30 40 30 -20 46 -2 -2 --6 -8 the…

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Q: Graph the following piecewise functions and discuss continuity: f(x)=√-3x+1, x 2

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Q: 2. Same question for in the case b = TNOT 2 Find the condition on b (if any) so that the system is…

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Q: Use the graph to find the following Q O (a) the domain off (b) the range of f (c) the x-intercepts…

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Q: 14. 15. Given f(x, y, z) = x²y³z − 3xy²z³ + 5x²z - y³z, find fxyz z = x² + x − 3xy + y³ − 5, find…

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Q: dx 3x+2y <=C Ans: 3e-2 +2e³x.

A: Given that the differential equation dydx=e3x+2y

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Q: Using the Parseval's relation to evaluate :- `x² dx (x² +1) of

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Q: 4. Solve: y³ dx + (x-1) dy = 0 1+2y In |x-1|=ky²2 1-2 y² mm |x-1|=ky² 1-2y In x + 1) = ky 1-2 y ln…

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Q: 4. Transform the integral formula [[+++] f(0)+3f 1 8 so that it can be used for f(x)dx. 3

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Q: ring (R₂, +',.'). prove that f-¹(S) subring of a ring (R₁, +,.)? Let f be a homomorphism from a ring…

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Q: Ex.3. Find t

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