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Use the auxiliary equation k2-5k+6=0. Solving this gives roots k=2 and k=3, which are real and distinct roots. This means that the complementary function is of the form y=Ae^(k1x)+Be...
Firstly, we note that there are 4 key steps for any proof by induction. (1) Basis : check the statement works for n=1. (2) Assumption : assume the statement is true for n=k. (3) Induction : prove the stat...
For f(x) to be an increasing function at x, the derivative of f(x) must be greater than 0. So, the answer to this question will be revealed by solving the equation f'(x) > 0 for x.By differentiating th...
Question: A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4 metres. Calculate the maximum speed of the particle. ...
Any odd integer can be represented by 2m+1 for some integer m (can prove that 2m+1 is always an odd number if needed). (2m+1)2=4m2+2m+2m+1=4m2+4m+1=4m(m+1)+1 simple factor...
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