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aalyn [17]
2 years ago
8

Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter UNDEFINED.)

Mathematics
1 answer:
juin [17]2 years ago
7 0

Answer:

Undefined.

Step-by-step explanation:

We want to find the slope of the graph of the equation:

\displaystyle x^2 - y^2 = 81

At the point (9, 0).

In other words, we want to evaluate dy/dx when <em>x</em> = 9 and <em>y</em> = 0.

Find dy/dx. We can take the derivative of both sides with respect to <em>x: </em>

\displaystyle \begin{aligned} \frac{d}{dx}\left[ x^2 - y^2\right] = \frac{d}{dx}\left [ 81\right] \\ \\ 2x - 2y \frac{dy}{dx} &= 0 \\ \\ \frac{dy}{dx} = \frac{x}{y}\end{aligned}

Then the slope of the graph at the point (9, 0) will be:

\displaystyle \begin{aligned} \frac{dy}{dx}\Big|_{(9, 0)} &= \frac{(9)}{(0)} \\ \\ &= \text{Und.}\end{aligned}

In conclusion, the slope of the graph at the point (9, 0) is undefined.

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Answer:

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3 years ago
Please help me with 8, 9, and 10 thanks! Show work too
Harrizon [31]
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Step-by-step explanation:

6 0
3 years ago
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tresset_1 [31]
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