The electric potential due to a point charge q at the origin is given by
![v= \frac{q}{4 \pi \epsilon _{0} r} = \frac{q}{4 \pi \epsilon _{0} \sqrt{x^{2}+y^{2}+z^{2}} }](https://tex.z-dn.net/?f=v%3D%20%5Cfrac%7Bq%7D%7B4%20%5Cpi%20%5Cepsilon%20_%7B0%7D%20r%7D%20%3D%20%5Cfrac%7Bq%7D%7B4%20%5Cpi%20%20%5Cepsilon%20_%7B0%7D%20%20%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%2Bz%5E%7B2%7D%7D%20%7D%20)
The x-component of electric field is
![e_{x} = - \frac{\partial v}{\partial x} = -\frac{q}{4 \pi \epsilon {0}}(- \frac{1}{2}) \frac{2x}{(x^{2}+y^{2}+z^{2})^{3/2}} = \frac{qx}{4 \pi \epsilon _{0} (x^{2}+y^{2}+z^{2})^{3/2}}](https://tex.z-dn.net/?f=e_%7Bx%7D%20%3D%20-%20%5Cfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20x%7D%20%3D%20-%5Cfrac%7Bq%7D%7B4%20%5Cpi%20%20%5Cepsilon%20%7B0%7D%7D%28-%20%5Cfrac%7B1%7D%7B2%7D%29%20%5Cfrac%7B2x%7D%7B%28x%5E%7B2%7D%2By%5E%7B2%7D%2Bz%5E%7B2%7D%29%5E%7B3%2F2%7D%7D%20%3D%20%20%5Cfrac%7Bqx%7D%7B4%20%5Cpi%20%20%5Cepsilon%20_%7B0%7D%20%28x%5E%7B2%7D%2By%5E%7B2%7D%2Bz%5E%7B2%7D%29%5E%7B3%2F2%7D%7D%20%20%20%20)
Answer:
Answer:
3/4
Step-by-step explanation:
9514 1404 393
Answer:
- y = 0
- A all real numbers
- E y > 0
- infinity
Step-by-step explanation:
1. The horizontal asymptote is the y-value the function approaches, but does not reach. That value is y = 0. This equation is the equation of that asymptote.
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2. The domain is the horizontal extent of the graph. It covers "all real numbers." (A)
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3. The range is the vertical extent of the graph. As we said in part 1, the value y = 0 is never reached, so the vertical extent (range) is y > 0 (E).
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4. The graph extends upward indefinitely as x extends to the left indefinitely. That is, y → infinity.
Answer:
The greatest possible error for the measurement 3.2 cm is 0.05 cm.
Step-by-step explanation:
We have given that,
Bruce measured a buckle as 3.2 cm using the ruler
We have to find,
What is the greatest possible error?
Solution is given by,
The greatest possible error is defined as the error is half of the measuring unit.
Bruce measured a buckle as 3.2 cm using the ruler.
The measuring unit is nearest tenth of a cm or 0.1 cm.
The greatest possible error is half of 0.1.
i.e. ![GPE=\frac{0.1}{2}](https://tex.z-dn.net/?f=GPE%3D%5Cfrac%7B0.1%7D%7B2%7D)
![GPE=0.05}](https://tex.z-dn.net/?f=GPE%3D0.05%7D)
Therefore, The greatest possible error for the measurement 3.2 cm is 0.05 cm.