1. Evaluate the integrals below. 5x²-x +3 (a) J x³ + x (b) [√v √√√x – 1 dx dx

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Q: 3. (a) Use the Binomial Theorem to expand and simplify (3a²-4b)6

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Q: Part 2. Solutions to Some First Order DE. Solve the following DE: y 3. y' = 3x² - y(1) = 5

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A: Cauchy integral formula for higher order derivative is :-fn(z0)=n!2πi∫cf(z)(z-z0)n+1dzwhere c is a…

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Q: Find the limit: lim (z,y) → (3,3) 4x4 - 4y¹ x² - y²

A: The given limit is: limx,y→3,34x4-4y4x2-y2  To find the value of the limit.

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A: p(x) = ax2+bx+c passes through point (1,7) , (-1,13) and (2,7). So, Form three equation using, p(1)…

Q: 9) xdy- ydx = (x² + y ² ) ex dx a) artan. * =* b) arctan X = ţ c) auctan $ d) none of the above etc…

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Q: Eliminate the arbitrary constants of the following. Simplify your answers.  10. y = c1e^x + c2e^-x +…

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Q: Find the angle (where 0° ≤0 ≤ 180°) between the following vectors. 0 u 9, 15 >, degrees 0 ||

A: here we have to find angle between two vector  use formula  cosθ = u*v/[u][v] [u] = 92 +(-15)2 [u] =…

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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Q: 4. Consider the level curves for f(x, y) below X

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Q: 2. Which of the following definite integrals represents the area of the shaded region? A. S²(4-x²)…

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