Open or closed? because if it's closed then the the answer is D
This question can be solved primarily by L'Hospital Rule and the Product Rule.
I) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[2xcos(x)-x^2sin(x)]-2sin(x)cos(x)}{4x^3}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B2xcos%28x%29-x%5E2sin%28x%29%5D-2sin%28x%29cos%28x%29%7D%7B4x%5E3%7D%20)
II) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)]}{12x^2} \\ y= \lim_{x \to 0} \frac{2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x)}{12x^2}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B-2xsin%28x%29%2B2cos%28x%29%5D-%5B2xsin%28x%29%2Bx%5E2cos%28x%29%5D-%5B2cos%5E2%28x%29-2sin%5E2%28x%29%5D%7D%7B12x%5E2%7D%20%5C%5C%20y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B2cos%28x%29-4xsin%28x%29-x%5E2cos%28x%29-2cos%5E2%28x%29%2B2sin%5E2%28x%29%7D%7B12x%5E2%7D)
III) Product Rule and L'Hospital Rule:
![]y= \alpha + \beta \\ \\ \alpha =\lim_{x \to 0} \frac{-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)]}{24x} \\ \beta = \lim_{x \to 0} \frac{4sin(x)cos(x)+4sin(x)cos(x)}{24x} \\ \\ y = \lim_{x \to 0} \frac{-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x)}{24x}](https://tex.z-dn.net/?f=%5Dy%3D%20%5Calpha%20%2B%20%5Cbeta%20%5C%5C%20%5C%5C%20%5Calpha%20%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-2sin%28x%29-%5B4sin%28x%29%2B4xcos%28x%29%5D-%5B2xcos%28x%29-x%5E2sin%28x%29%5D%7D%7B24x%7D%20%5C%5C%20%5Cbeta%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B4sin%28x%29cos%28x%29%2B4sin%28x%29cos%28x%29%7D%7B24x%7D%20%5C%5C%20%20%5C%5C%20y%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-6sin%28x%29-4xcos%28x%29-2xcos%28x%29%2Bx%5E2sin%28x%29%2B8sin%28x%29cos%28x%29%7D%7B24x%7D)
IV) Product Rule and L'Hospital Rule:
![y = \phi + \varphi \\ \\ \phi = \lim_{x \to 0} \frac{-6cos(x)-[-4xsin(x)+4cos(x)]-[2cos(x)-2xsin(x)]}{24x} \\ \varphi = \lim_{x \to 0} \frac{[2xsin(x)+x^2cos(x)]+[8cos^2(x)-8sin(x)]}{24x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cphi%20%2B%20%5Cvarphi%20%5C%5C%20%20%5C%5C%20%5Cphi%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%20%5Cfrac%7B-6cos%28x%29-%5B-4xsin%28x%29%2B4cos%28x%29%5D-%5B2cos%28x%29-2xsin%28x%29%5D%7D%7B24x%7D%20%20%5C%5C%20%5Cvarphi%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%20%5Cfrac%7B%5B2xsin%28x%29%2Bx%5E2cos%28x%29%5D%2B%5B8cos%5E2%28x%29-8sin%28x%29%5D%7D%7B24x%7D%20)
V) Using the Definition of Limit:
For example let’s use something simple.
1+1 < 3+6
Why is this?
Because 1 +1 = 2 and that is less than 3 + 6 which is 9. Next time, apply this to something harder you might learn. I hope this helped <3
Answer:
shown below
Step-by-step explanation:
1. The pair of angles shown in your diagram are vertical angles. Vertical angles are each of the pairs of opposite angles made by two intersecting lines. The pairs of vertical angles have the exact same measurement. Therefore, 5x and 100 must have the same degree measurement, or 100 degrees. Thus, 5x must equal 100, so 5x = 100, and x would be 20 degrees.
2. The diagram shows a right angle (90 degrees) formed by 3x degrees and 39 degrees. 3x and 39 are complementary, which means they add up to 90, not 180 (that's supplementary). Thus, 3x + 39 = 90, 3x = 51, and x = 17 degrees.
3. The diagram shows a 180-degree angle formed by 6x degrees and 2x + 8 degrees. This means that 6x + (2x+8) equals 180. 6x + 2x + 8 = 180 and 8x + 8 = 180, 8x = 172, and x = 21.5 degrees.
4. A angle's supplement is basically 180 - (angle measure), because you are finding the angle that when formed with the original angle creates a 180 degree angle. Thus, the supplement angle would be 180 - 47 which is 133 degrees.
5. The angles 115 and (5x-10) create a 180 degree angle, which means that 115 + (5x-10) = 180. Thus, x = 15.
