NUMERICAL METHODS (mei ocr) - HELP IF YOU CAN! Watch

Kaya_01
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Jan 2010 paper:

(Q3) Given that f(x)=x^3-x^2+1, find f(0.5).

Use the forumla f(x+h)≈f(x)+hf '(x) to show that

f(0.5+h)≈0.875-0.25h

hence determine the approximate range of values of x for which f(x)=0.875 correct to 3 decimal places.

Also,

Q7)

Show that the equation x = 3 sin x can be rearranged into the form

x = sin x + 2/3 x


If you have sufficient knowledge on numerical methods, and you know how to do these questions then please help! Much appreciated! thanks
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roar558
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3. To find f(0.5) sub 0.5 for x, you should end up with 0.875
differentiate f(x) to find f'(x) then use it in the formula f(x+h)is about = f(x)+hf'(x) and you should get the answer given

7. first divide both sides by 3 you end up with (x/3)=sinx
another way of writing (x/3) is x-(2/3)x so add (2/3)x to both sides
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