Function:
Linear function: y=kx+b
Quadratic function: y = ax 2+bx+c
Inverse proportional function: y=k/x direct proportional function; Y=kx when b=0.
Exponential function: y = a x(a >；; 0 and not equal to 1)
Logarithmic function: y = loga x loga1= ologaa =1.
Series:
Arithmetic series: the tolerance mark is D.
General formula: an(n low) = a1+(n+1) d.
Item: A=a+b/2 (A-a=A-b)
Sum of the first n items: Sn=n(a 1+a2)/2 or Sn=na 1+n(n- 1)d/2.
Geometric series: the common ratio is written as Q.
General formula: a n is n- 1 power, and the base number = a1q.
The first n terms and formulas: sn = a1(1n power of-q)/1-q or Sn=a 1-an(n is base) q/ 1-q (q is not equal to 0). It is very important to write down the first n terms and formulas of a series.
Derivation:
Find the derivative of the function y=f(x) at x0:
① Find the increment δ y = f (x0+δ x)-f (x0) of the function;
② Find the average change rate;
③ Seek the limit and derivative.
Derivative formulas of several common functions;
① C'=0(C is a constant);
②(x^n)'=nx^(n- 1)(n∈q)；
③(sinx)' = cosx；
④(cosx)' =-sinx；
⑤(e^x)'=e^x；
⑥ (a x)' = a A Xin (ln is natural logarithm).
Four algorithms of derivative:
①(u v)' = u ' v '；
②(uv)' = u ' v+ uv '；
③(u/v)'=(u'v-uv')/ v^2。
Derivative function of composite function;
Let y = u (t) and t = v (x), then y'(x) = u'(t)v'(x) = u'[v(x)] v'(x).
For example: y = t^2, t = sinx, then y'(x) = 2t * cosx = 2sinx*cosx = sin2x.
The sum formula of two angles:
sin(a+B)=sinacosB+cosasinB
sin(a-B)=sinacosB-cosasinB
cos(a+B)=cosacosB-sinasinB
cos(a-B)=cosacosB+sinasinB
tan(a+B)=(tana+tanB)/ 1-tana tanB
tan(a-B)=(tana-tanB)/ 1+tana tanB
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