Answer:
A.
Step-by-step explanation:
Because they are both subtracting, both lines have to go to the left
Answer:
for the first one I think it is -5/-2 second is 1/-4 third one is 2/1 this may not be correct
Step-by-step explanation:
Answer:
Step-by-step explanation:
s + r = 181
r = 119 + s
s + 119 + s = 181
2s + 119 = 181
2s = 181 - 119
2s = 62
s = 62/2
s = 31 <=== there are 31 senators
r = 119 + s
r = 119 + 31
r = 150 <=== there are 150 representatives
Answer:
Yaa it's true
Step-by-step explanation:
-56=-56
from both side u get the same answer
![sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0](https://tex.z-dn.net/?f=sin~%20x%20%5Capprox%20x%20~%20~%5Csf%7Bas%7D~~%20x%20%5Crightarrow%200)
We can replace sin x with x anywhere in the limit as long as x approaches 0.
Also,
![\large \lim_{ x \to 0 } ~ x^x = 1](https://tex.z-dn.net/?f=%5Clarge%20%20%5Clim_%7B%20x%20%5Cto%200%20%20%7D%20~%20%20x%5Ex%20%3D%201)
I will make the assumption that <span>log(x)=ln(x)</span><span>.
The limit result can be proven if the base of </span><span>log(x)</span><span> is 10.
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![\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{ \log( x^x) } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } ~~ \normalsize{\text{ substituting x for sin x } } \\~\\ \large = \frac{\lim_{x \to 0^{+}} (1) - \lim_{x \to 0^{+}} \left( x^{x}\right) }{ \log( \lim_{x \to 0^{+}}x^x) } = \frac{1-1}{\log(1)} = \frac{0}{0}](https://tex.z-dn.net/?f=%5Clarge%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B1-%20x%5E%7B%5Csin%20x%7D%20%7D%7Bx%20%20%5Clog%20x%20%7D%20%20%5C%5C~%5C%5C%20%20%5Clarge%20%3D%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B1-%20x%5E%7B%5Csin%20x%7D%20%7D%7B%20%5Clog%28%20x%5Ex%29%20%20%7D%20%20%20%5C%5C~%5C%5C%20%20%5Clarge%20%3D%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B1-%20x%5E%7Bx%7D%20%7D%7B%20%5Clog%28%20x%5Ex%29%20%20%7D%20%20~~%20%5Cnormalsize%7B%5Ctext%7B%20substituting%20x%20for%20sin%20x%20%7D%20%7D%20%5C%5C~%5C%5C%20%20%20%5Clarge%20%20%3D%20%5Cfrac%7B%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%281%29%20-%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cleft%28%20x%5E%7Bx%7D%5Cright%29%20%7D%7B%20%5Clog%28%20%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7Dx%5Ex%29%20%20%7D%20%3D%20%5Cfrac%7B1-1%7D%7B%5Clog%281%29%7D%20%20%20%3D%20%5Cfrac%7B0%7D%7B0%7D)
We get the indeterminate form 0/0, so we have to use <span>Lhopitals rule
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![\large \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } =_{LH} \lim_{x \to 0^{+}} \frac{0 -x^x( 1 + \log (x)) }{1 + \log (x) } \\ = \large \lim_{x \to 0^{+}} (-x^x) = \large - \lim_{x \to 0^{+}} (x^x) = -1](https://tex.z-dn.net/?f=%5Clarge%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B1-%20x%5E%7Bx%7D%20%7D%7B%20%5Clog%28%20x%5Ex%29%20%20%7D%20%3D_%7BLH%7D%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B0%20-x%5Ex%28%201%20%2B%20%5Clog%20%28x%29%29%20%7D%7B1%20%2B%20%5Clog%20%28x%29%20%20%7D%20%20%20%5C%5C%20%3D%20%5Clarge%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%28-x%5Ex%29%20%3D%20%5Clarge%20-%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%28x%5Ex%29%20%3D%20-1)
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Therefore,
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![\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } =\boxed{ -1}](https://tex.z-dn.net/?f=%5Clarge%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%7D%20%5Cfrac%7B1-%20x%5E%7B%5Csin%20x%7D%20%7D%7Bx%20%20%5Clog%20x%20%7D%20%20%3D%5Cboxed%7B%20-1%7D)
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