Use the Newton-Raphson iteration method to estimate the root of the following function employing an initial guess of x0 = 3.75: f(x) = x(x² – x – 10) – 8 = 0 (If a tolerance of 0.0003 is required)

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Q: f (t) = 3u(t) + 8(t – 2) + 8(t – 5) – u(t – 7)

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Q: (a) Find Z(H). (b) Prove that Z(H)=Q, Q is under addition.

A: This is a problem of Group Theory, Isomorphism.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: