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Calculate the shaded finite region between the curve and the axis for the curve: 3x^2 +11x -4 = 0

3x 2 +11x-4=0 #Factorise to find where the curve crosses the x axis (3x-1)(x+4)=0 #Each bracket equals 0 x=1/3, -4 #Integrate the curve between these two points to find the area enclosed in the curve [x 3 + ...
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Answered by Hugo F. • Maths tutor
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express (3x + 5)/(x^2 + 2x - 15) - 2/(x - 3) as a single fraction its simplest form

(x - 5) / (x 2 + 2x - 15)
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Answered by George H. • Maths tutor
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Why does the product rule for differentiating functions work?

Let k(x) = f(x)g(x) then k'(x) = limit as h --> 0 of: (h(x+h)-h(x))/h = lim (f(x+h)g(x+h) - f(x)g(x))/h We can factorise the numerator as: f(x+h)g(x+h) - f(x)g(x) =f(x+h)g(x+h) -g(x)f(x+h) + g(x)f(x+h)- f...
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Answered by Blaine V. • Maths tutor
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Given that y = 16x^2 + 7x - 3, find dy/dx [3 marks]

32x + 7
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Answered by Bodrul H. • Maths tutor
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Express (16x^2 + 4x^3)/(x^3 + 2x^2 - 8x) + 12x/(x-2) as one fraction in its simplest form.

Answer: 16x/(x - 2) Start with the numerator of the first fraction, 16x 2 + 4x 3 , take a factor of 4x 2 out to get 4x 2 (4 + x). Then look at the denominator of the fraction, x 3 + 2x 2 - 8x, immediately yo...
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Answered by Manon S. • Maths tutor
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