-x + 3/2 = -y know how to do the Y equals MX plus b
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Answer:
Step-by-step explanation:
Tan can be defined as: as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.
Using this we can define tan
A. Factor the numerator as a difference of squares:
c. As
, the contribution of the terms of degree less than 2 becomes negligible, which means we can write
e. Let's first rewrite the root terms with rational exponents:
![\displaystyle\lim_{x\to1}\frac{\sqrt[3]x-x}{\sqrt x-x}=\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto1%7D%5Cfrac%7B%5Csqrt%5B3%5Dx-x%7D%7B%5Csqrt%20x-x%7D%3D%5Clim_%7Bx%5Cto1%7D%5Cfrac%7Bx%5E%7B1%2F3%7D-x%7D%7Bx%5E%7B1%2F2%7D-x%7D)
Next we rationalize the numerator and denominator. We do so by recalling
In particular,
so we have
For
and 
, we can simplify the first term:
So our limit becomes
c. As
e. Let's first rewrite the root terms with rational exponents:
Next we rationalize the numerator and denominator. We do so by recalling
In particular,
so we have
For
So our limit becomes