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A circle with centre C(2, 3) passes through the point A(-4,-5). (a) Find the equation of the circle in the form (x-a)^2 + (y-b)^2=k

This question is aimed at A-Level Pure Core 1 students. A circle with centre C(2, 3) passes through the point A(-4,-5). Find the equation of the circle in the form (x-a)^2 + (y-b)^2 = k From the formula for ...
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Answered by Tilly C. • Maths tutor
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Differentiate x^3 − 3x^2 − 9x. Hence find the x-coordinates of the stationary points on the curve y = x^3 − 3x^2 − 9x

To differentiate, we bring the power down and decrease the power by 1. So x 3 becomes 3x 2 , -3x 2 becomes -6x, and -9x (which can be written as -9x 1 ) becomes -9. So y' = 3x 2 - 6x - 9 This equation tells ...
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Answered by Tutor105800 D. • Maths tutor
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Evaluate the following integral: (x^4 - x^2 +2)/(x^2(x-1)) dx

This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the fir...
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Answered by Nicholas H. • Maths tutor
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Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6x sin(2x). uv' = 6x^2 cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [...
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Answered by Kilian S. • Maths tutor
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Differentiate the function f(x)=2xsin3x

Use the product rule: u'v + uv' u = 2x V= sin3x u'= 2 v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x
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Answered by Thomas W. • Maths tutor
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