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Further Mathematics
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I don't understand how proof by mathematical induction works, can you help?

This took me some time to get my head around so I know what you mean. I always like to think of proof by induction like dominoes. Once you've pushed the first domino in line of dominos, you know it's goin...

JB
2147 Views

Solve the following complex equation: '(a + b)(2 + i) = b + 1 + (10 + 2a)i' to find values for 'a' and 'b'

The first step with this question is to expand all the brackets; this will produce the following equation:

2a + ai + 2b + bi = b + 1 + 10i + 2ai

The next step is to put all the terms which c...

SM
14307 Views

Find the general solution of the differential equation d^2y/dx^2 - 5*dy/dx + 4y = 2x

Solve complimentary function: Let y = emx then,
d2y/dx2 - 5dy/dx + 4y = 0
m2emx - 5memx + 4emx = 0 (substituting fo...

PM
12340 Views

In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?

The largest speed is obtained at the position of equilibrium.

v=Aw

So v= 2 x 1

     v=2ms-1

WC
2456 Views

A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

dy/dx = 9x^2 + 2ax + b

x = 2, dy/dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, dy/dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

AR
2344 Views

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