Forumet - gahhh. jag är kass på matte! [cry]

gahhh. jag är kass på matte! [cry]

711 0 12
hjälper kompis. har seriöst glömt hur man löser det här talet:

bestäm ekvationen för tangenten till kurvan:

y=3 sin2x - cos2x

då x = 0.75π (3pi/4)

jag får:

y=3 sin2x - cos2x
y'= 2*3cos2x + 2*2sin2x
y' = 6cos2x + 4sin2x

gör om till en funktion:
f'(x) = 6cos2x + 4sin2x
f'(0.75π) = -2

k = -2

men hur gör jag för att få ekv till tangenten därifrån? det är blankt [shake]

Spana också in:

Karl Bertil Jonsson:


Ekvation för kurva: y = f(x)
Ekvation för tangent: y = g(x)
Koordinater för tangeringspunkt: (x[0],y[0])

k = (g(x)-y[0])/(x-x[0])
y[0] = f(x[0])
k = f'(x[0])

k = (g(x)-y[0])/(x-x[0])
y[0] = f(x[0])
k = f'(x[0])
f'(x[0]) = (g(x)-f(x[0]))/(x-x[0])

f'(x[0]) = (g(x)-f(x[0]))/(x-x[0])
f'(x[0])(x-x[0]) = g(x)-f(x[0])
f'(x[0])x-f'(x[0])x[0] = g(x)-f(x[0])
f'(x[0])x-f'(x[0])x[0]+f(x[0]) = g(x)
g(x) = f'(x[0])x-f'(x[0])x[0]+f(x[0])

g(x) = f'(x[0])x-f'(x[0])x[0]+f(x[0])

f(x) = 3(sin(2x))-cos(2x)
x[0] = (3/4)π

f(x) = 3(sin(2x))-cos(2x)
f'(x) = 3*2(cos(2x))+2(sin(2x))
f'(x) = 6(cos(2x))+2(sin(2x))
f'(x) = 2(sin(2x))+6(cos(2x))

f(x) = 3(sin(2x))-cos(2x)
f(x[0]) = 3(sin(2x[0]))-cos(2x[0])

f(x[0]) = 3(sin(2x[0]))-cos(2x[0])
x[0] = (3/4)π
f(x[0]) = 3(sin(2(3/4)π))-cos(2(3/4)π)
f(x[0]) = 3(sin((2*3/4)π))-cos((2*3/4)π)
f(x[0]) = 3(sin((6/4)π))-cos((6/4)π)
f(x[0]) = 3(sin((3/2)π))-cos((3/2)π)

f(x[0]) = 3(sin((3/2)π))-cos((3/2)π)
sin((3/2)π) = -1
cos((3/2)π)) = 0
f(x[0]) = 3(-1)-0
f(x[0]) = -3

f'(x) = 2(sin(2x))+6(cos(2x))
f'(x[0]) = 2(sin(2x[0]))+6(cos(2x[0]))

f'(x[0]) = 2(sin(2x[0]))+6(cos(2x[0]))
x[0] = (3/4)π
f'(x[0]) = 2(sin(2(3/4)π))+6(cos(2(3/4)π))
f'(x[0]) = 2(sin((2*3/4)π))+6(cos((2*3/4)π))
f'(x[0]) = 2(sin((6/4)π))+6(cos((6/4)π))
f'(x[0]) = 2(sin((3/2)π))+6(cos((3/2)π))

f'(x[0]) = 2(sin((3/2)π))+6(cos((3/2)π))
sin((3/2)π) = -1
cos((3/2)π)) = 0
f'(x[0]) = 2(-1)+6*0
f'(x[0]) = -2+0
f'(x[0]) = -2

g(x) = f'(x[0])x-f'(x[0])x[0]+f(x[0])
x[0] = (3/4)π
f(x[0]) = -3
f'(x[0]) = -2
g(x) = -2x-(-2)(3/4)π+(-3)
g(x) = -2x+(2*3/4)π-3
g(x) = -2x+(6/4)π-3
g(x) = -2x+(3/2)π-3
g(x) = -2x-3+(3/2)π

g(x) = -2x-3+(3/2)π