Saturday, 30 March 2013

Lesson summary 28/3 Jia Qi

Exponential Growth (a•xn)

General Formula: y=a•xn

If a =1, n∈ℤ , -2 ≦ n ≦ 3

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If n=-2
y=1/x2
y>0 , x≠ 0 (Asymptote at x=0)
















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If n=-1
y=1/x


x≠ 0 (Asymptote at x=0)

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If n=0
y=1/x2


Linear (y=mx+c)

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If n=1
y=x (Linear)



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If n=2
y=x(Quadratic)


Turning point: (0,0)
















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If n=3  Case 1
y=x3(Cubic)


Gradient = 0 at x=0


















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If n=3  Case 2
y=x3+x(Cubic)


















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If n=3  Case 3
y=x(x-1)(x+3)(Cubic)
3 real and different roots
2 turning points

















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Limit Theory

y=1/x

As x ---->0
    y ---->

x = 1 ,  y = 1
x = 1/2 , y = 2

x = 1/4 ,  y = 4
x = 1/10 , y = 10
x = 1/1000 , y = 1000

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