Hvad er ligningen af linjen, der er normal til f (x) = cscx + tanx-cotx ved x = -pi / 3?

Svar:

#Y = - (3x) /14-2.53#

Forklaring:

# "Tangent": d / dx f (x) = f '(x) #

# "Normal": - 1 / (f (x)) = - 1 / (d / dx cscx + tanx-cotx) = - 1 / (d / dx cscx + d / dx tanx - d / dx cotx) = - 1 / (- cscxcotx + sek ^ 2x + csc ^ 2x) #

# -1 / (f '(- pi / 3)) = - 1 / (- csc (-pi / 3) barneseng (-pi / 3) + sec ^ 2 (-pi / 3) + csc ^ 2 (- pi / 3)) = - 1 / (14/3) = - 3/14 #

# Y = mx + c #

#F (a) = ma + c #

#csc (-pi / 3) + tan (-pi / 3) -cot (-pi / 3) = - pi / 3 (-3/14) + c #

# c = csc (-pi / 3) + tan (-pi / 3) -cot (-pi / 3) + pi / 3 (-3/14) #

# C = -2,53 #

#Y = - (3x) /14-2.53#