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The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0. Find y: y = r sin(x) = 3a(1 + cos(x))(sin(x)) Differentiate y with respect to x dy/dx = 3a[(2cos(x) - 1)(cos(x) + 1)] = 0 Solve equation 2cos(x)- 1 = 0 cos(x) = 1/2 ...
SS
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Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.

Firstly set 2sinhx+3coshx=5Now using the exponential definitions of sinhx and coshx rewrite the equation to give:2(1/2(e^x-e^-x))+3(1/2(e^x+e^-x))=5Simplify the equation by expanding out the brackets, multip...
ES
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What is the range of solutions for the inequality 2(3x+1) > 3-4x?

When it comes to answering questions about inequalities, it is important to remember the signs and what they represent. In this instance, we need to find a range of solutions where 2(3x+1) is greater than 3-...
SK
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How do I use proof by induction?

Induction is an incredibly powerful form of proof. As such, it is essential to be able to call upon such a tool if you want to study any higher form of mathematics. The basic structure of the method is as fo...
AD
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How do I find the limit as x-->infinity of (4x^2+5)/(x^2-6)?

Here you will deal with all problems of the same type in a very similar way. Intuition first tells us that we can’t really find the limit, as both the top (4x 2 +5), and the bottom (x 2 -6) parts of the frac...
AD
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