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Point K(8,-5) lies on the circle x^2 +y^2 - 12x - 6y - 23. find the equation of the tangent at K.

First, find the centre of the circle. Since we know the equation of the circle, we know that the centre (-g,-f) comes from the part of the equation -12x-6y, where -12=2g and -6=2f. Therefore, to get the cent...
CM
Answered by Catriona M. • Maths tutor
2791 Views

Differentiate y = 3x4-8x3-3

y = 3x 4 -8x 3 -3dy/dx = (3 x 4)x 3 -(8 x 3)x 2 dy/dx = 12x 3 - 24x 2
BG
Answered by Bhavya G. • Maths tutor
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Evaluate the integral ∫2x√(x^2 +1) dx

The first step is deciding on the method of integration. For this integral it makes the most sense to use substitution.Let u = x 2 + 1Differentiate w.r.t x => du/dx = 2xRearrange for dx=> du/2x = dx Su...
SC
Answered by Sam C. • Maths tutor
12028 Views

Evaluate the following : ∫ln(x) dx

Integrate by parts:u = ln(x) u' = 1/x v' = 1 v = xBy parts formula: uv - ∫u'v dx Therefore we have: x ln(x) - ∫x 1/x dx = x ln(x) - ∫1 dx = x ln(x) - x (+c)
SM
Answered by Saaqib M. • Maths tutor
6908 Views

Find x in the following equation: 4x + 8 -2x = 10

First combine the x-parts of the equation: 4x - 2x = 2x Next move the "number parts" so they are all on the same side: 2x + 8 = 10 ---> 2x = 2 Then divide through by 2 to move the 2 from the 2x ...
EM
Answered by Elizabeth M. • Maths tutor
5227 Views