To change 0.0002 to scientific notation, move the decimal to the right 4 places so that you get 2. The exponent on the base 10 will be -4 because the decimal was moved to the right 4 places

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3 years ago

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Can anyone help me understand how to evaluate the limit of this complex fraction?

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Answer:

-1/9

Step-by-step explanation:

$\lim_{x \to 3} \frac{1/x-1/3}{x-3}$

For simplicity, let's multiply top and bottom by 3x:

$\lim_{x \to 3} \frac{3-x}{3x(x-3)}$

Factor out a -1:

$\lim_{x \to 3} \frac{-(x-3)}{3x(x-3)}$

Divide top and bottom by x−3:

$\lim_{x \to 3} \frac{-1}{3x}$

Evaluate the limit:

$\frac{-1}{3(3)}\\-\frac{1}{9}$

It's important to note that the function doesn't exist at x = 3. As x <em>approaches</em> 3, the function <em>approaches</em> -1/9.

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3 years ago