Answer:
d. Perpendicular line through a point on a line
Step-by-step explanation:
We presume you're looking for a description of line HG.
The construction makes points H and G equidistant from points D and B, and it puts point C on the line HG. This makes HG perpendicular to AB, and it makes HG contain point C. Thus we have a perpendicular through a point on a line.
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Nothing about this construction creates an equilateral triangle or hexagon. The perpendicular is through points H and G, which are off the line AB, but we did not start with those. A perpendicular through an off-line point is constructed differently.
Answer:
3.45
Step-by-step explanation:
pretty sure
7 x 6 = 42 x 5 = 210 x 8 = 1,680 x 4 = [ 6,720 ]
Answer:
1. shown below
2. ![\frac{-1}{\sqrt{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D)
Step-by-step explanation:
We say
exists if the limit remains the same along every path.
Here, f is a function on two variables defined on a disk that contains the point (a,b).
1.
Along y-axis i.e., x = 0:
![\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{y\rightarrow 0}\frac{0}{\sqrt{0^2+y^2}}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%28a%2Cb%29%7Df%28x%2Cy%29%3D%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%280%2C0%29%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%7D%7D%3D%5Cdisplaystyle%20%5Clim_%7By%5Crightarrow%200%7D%5Cfrac%7B0%7D%7B%5Csqrt%7B0%5E2%2By%5E2%7D%7D%3D0)
Along x-axis i.e., y = 0:
![\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{x^2+0^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{x}=-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%28a%2Cb%29%7Df%28x%2Cy%29%3D%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%280%2C0%29%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%7D%7D%3D%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%200%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7Bx%5E2%2B0%5E2%7D%7D%3D%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%200%7D%5Cfrac%7B-x%7D%7Bx%7D%3D-1)
As the limit is not the same along different paths, so limit does not exist.
2.
Along the path x = y:
![\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{x^2+x^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{2}x}=\frac{-1}{\sqrt{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%28a%2Cb%29%7Df%28x%2Cy%29%3D%5Cdisplaystyle%20%5Clim_%7B%28x%2Cy%29%5Crightarrow%20%280%2C0%29%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%7D%7D%3D%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%200%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7Bx%5E2%2Bx%5E2%7D%7D%3D%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%200%7D%5Cfrac%7B-x%7D%7B%5Csqrt%7B2%7Dx%7D%3D%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D)