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Maths
A Level

The curve C has an equation y = sin(2x)cos(x)^2. Find dy/dx. Find normal to curve at x = pi/3 rad, giving answer in exact form.

Student should use a combination of trigonometric identities, product rule and chain rule to find dy/dx.This can be done by applying product rule, obtainingdy/dx = sin(2x). d[cos(x)^2]/dx + cos(x)^2. d[si...

SC
Answered by Sunchi C. Maths tutor
3600 Views

Solve the equation 3 sin^2 theta = 4 cos theta − 1 for 0 ≤ theta ≤ 360

I would convert the sin squared theta into a cos squared theta using identity that sin sq + cos sq = 1This would then give me a quadratic equation which I would substitute X = cos thetaThen I would solve ...

ML
Answered by Mario L. Maths tutor
8375 Views

The circle C has centre (3, 1) and passes through the point P(8, 3). (a) Find an equation for C. (b) Find an equation for the tangent to C at P, giving your answer in the form ax + by + c = 0 , where a, b and c are integers.

A)1) Draw a diagram of the circle displaying the centre and perimeter points along with their respective co-ordinates.2) Write down the equation for a circle labelling the centre and perimeter points. 3) ...

PV
Answered by Patrick V. Maths tutor
7759 Views

How would you integrate ln(x)

It can seem tricky to integrate ln(x), as there is no obvious solution to do it.It is, however, quite simple to do if you use the 'by parts' method.If you have y=ln(x)Set u=ln(x) and dv/dx=1That gives du/...

AC
Answered by Adam C. Maths tutor
2771 Views

y=e^2x-11e^x+24 Find the stationary point, nature of the stationary point, the x-intercepts and the y-intercept (calculator allowed)

Stationary point:
dy/dx = 2e^2x - 11e^x =0
2e^2x = 11e^x
e^x=5.5 (can divide by e^x since e^x > 0 for all x)
x=ln(5.5), y=5.5^2-115.5+24=-6.25
Answer:

AJ
Answered by Asmita J. Maths tutor
2828 Views

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