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Farid S.'s Resources


derivation of sin(3x)/(1+x^2) (answer)

Quotient rule: "low d'high - high d'low, square the denominator and away we go"   This essentially means "[ (bottom function)*(derivative of the top function) - (top function)*(derivative of the bottom function) ] / (bottom function)2   Applying the quotient...


What are the roots of the equation (answer)

You have to use the quadratic equation to solve this problem.   The general formula for the quadratic equation is x = {-b +- sqrt [ b2 - 4(a)(c) ]} / (2a)   Applying this formula to this problem, we get: {-(-7) +- sqrt [ (-7)2 - 4(2)(4) ]} / (2a)   From...


3*(2x^2+6x+3) (answer)

This is actually pretty straight forward.  Just multiply 3 all the way through.   So, we get 6x^2 + 18x + 9.


Find f(h(x)) (answer)

Awesome, thanks for posting an example.   So in this problem, we want to replace the x in f(x) with h(x).  That would give us f(12/x).  So in the function for f(x), where there is an x, we replace it with (12/x).   So, f(h(x)) becomes f(12/x) = (12/x)^2 +...


Find the exact circumference (answer)

Hi Theresa,   Circumference =  2*pi*r and area = pi*r*r.   So, the circumference would be 2*pi*11cm = 22pi cm.   Furthermore, the area would be pi*11cm*11cm = 121pi cm2   Hope this helps.


find the inverse (answer)

Hi Dalia,   To find the inverse of the function the first step is to solve for t.  To do this, get t by itself.   We get √(3t) = y - 2.   Squaring both sides, we get 3t = y2 - 4y + 4.   Dividing both sides by 3, we get t =...