Limit sin2x/sin3x
x>0

see picture

Step-by-step explanation:

Explanation:

Since we have an indeterminate form of type 00, we can apply the l'Hopital's rule:

limx→0  sin(2x)/sin(3x)=  limx→0  d/dx(sin(2x))/ d/dx(sin(3x))

limx→0  d/dx(sin(2x))/d/dx(sin(3x) ) = limx→02cos(2x)/3cos(3x)

Substitute the variable with the value:

limx→02cos(2x)3cos(3x)=(23)

Therefore,

limx→0sin(2x)sin(3x)=23

limx→0sin(2x)sin(3x)=2/3

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18