Analiza I: 3. kolokvij - plonkec na A4
TRIGONOMETRIJA
| |0 |30 |45 |60 |90 |
|sin |0 |½ |√2/2 |√3/2 |1 |
|cos |1 |√3/2 |√2/2 |½ |0 |
|tg |0 |√3/3 |1 |√3 |( |
sin (a + b) = sin a cos b + cos a sin b
cos (a + b) = cos a cos b + sin a sin b
sin 2a = 2 sin a cos a
cos 2a = cos2a - sin2a
sin a+sin b=2sin½(a+b)cos½(a-b)
sin a-sin b=2sin½(a-b)cos½(a+b)
cos a+cos b=2cos½(a+b)(cos½(a+b)
cos a-cos b=-2sin½(a+b)(sin½(a-b)
cos a(cos b=½(cos(a+b)+cos(a-b))
sin a(sin b=½(cos(a-b)-cos(a+b))
sin a(cos b=½(sin(a+b)+sin(a-b))
[pic][pic]
1+tg2x=cos-2x
tg 2x=2tgx/(1-tg2x)
[pic]
sinxcosx= 1/2 sin2x
cos2x = cos2x-sin2x = 2cos2x-1
cos2x = 1/2 (1+cos2x)
sin2x = 1/2 (1-cos2x)
|y |sin y |cos y |
|½(-x |cos x |sin x |
|(+x |-sin x |-cos x |
|(-x |sin x |-cos x |
|3x |3sin(x)-4s|4cos3x-3co|
| |in3x |sx |
|-x |-sin x |cos x |
ODVODI:
Definicija:
[pic]
(f(g)' = f'+g'
(f(x)(g(x))' = f'(x)g(x)+f(x)(g'(x)
[pic]
(g(f(x)))' = g'(f(x))(f'(x)
(sin x)' = cos x
(cos x)' = -sin x
(tg x)' = 1/cos2x
(ctg x)' = -1/sin2x
(ln x)' = 1/x
(logax)' = 1/(xln a)
(ex)' = ex
ax = ax ln a
(arccos x)' = 1/((1-x2)
(arctg x)' = 1/(1+x2)
(ch x)' = sh x
(sh x)' = ch x
(th x)' = 1/ch2x
(f-1x)' = 1/f'(f-1x)
f je zv. v x, če (ε>0 (δ>0 da je za (y |f(x) - f(y)|0, da je za (x, x'(I velja |f(x) - f(x')|0), konkavnosti( ................
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