Question 1c) i) Given the quadrature formulae, ,3 | f(x)dx = h[ny, + Ayo +5 23 A²yo + 6 4 n³ + n² ) a³yo + .…] 2 Explain why, Explain why, f(x)dx = h[y, + Ay.] at n = 1 and not, S* f(x)dx = h[yo +Ay -A³yo] from above %3D 12

Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

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Q: Finds 2) S 12x-31 dx

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Q: True or false: True False d dx 2 + ² = 1/2 2+ - X

A: d(xn)dx=nxn-1d dx(constant)=0f(x)=2+1x

Q: Evaluate: d dxJ (21² + 5)² dt.

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Q: - 4x + 30 -dæ Evaluate (x – 5)(x + 5) + C

A: To solve the given integral first break the integrand into the simple expression using partial…

Q: Differentiate. f(x) = In (4x+5)(x+8)5 (1-4X)6

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Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

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Q: dy Find if dx (² + 7)* 3 5,

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Q: Differentiate these using the product rule. Write your answers in fully factorised form with the…

A: NOTE According to our guidelines we are supposed to answer only one question and three subparts.…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.