Find the horizontal and vertical asymptotes of f(x). f(x) equals = StartFraction 6 x Over x plus 2 EndFraction 6x x+2 Find the
2 answers:
Answer:
The horizontal asymptote can be described by the line y = 6
The vertical asymptote can be described by the line x = -2
Step-by-step explanation:
* <em>Lets the meaning of vertical and horizontal asymptotes</em>
- <u><em>Vertical asymptotes</em></u> are vertical lines which correspond to the zeroes
of the denominator of a rational function
- <u><em>A horizontal asymptote</em></u> is a y-value on a graph which a function
approaches but does not actually reach
- If the degree of the numerator is less than the degree of the
denominator, then there is a horizontal asymptote at y = 0
- If the degree of the numerator is greater than the degree of the
denominator, then there is no horizontal asymptote
- If the degree of the numerator is equal the degree of the denominator,
then there is a horizontal asymptote at y = leading coefficient of the
numerator ÷ leading coefficient of the denominator
* <em>Lets solve the problem</em>
∵
∵ The numerator is 6x
∵ The denominator is x + 2
∴ The numerator and the denominator have same degree
∵ The leading coefficient of the numerator is 6
∵ The leading coefficient of the denominator is 1
∴ There is a horizontal asymptote at y = 6/1
∴ <em>The horizontal asymptote can be described by the line y = 6</em>
- Put the denominator equal zero to find its zeroes
∵ The denominator is x + 2
∴ x + 2 = 0
- Subtract 2 from both sides
∴ x = -2
∴ <em>The vertical asymptote can be described by the line x = -2</em>
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Answer:
7.789×10^-2 = 0.07789 cm
Step-by-step explanation:
Your calculator can find the difference of the two given diameters and express it in any format you like.
The attached image of a calculator display shows the difference of the cell diameters is 0.07789 = 7.789×10^-2 cm.
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The difference of two numbers with different exponents is found by first adjusting the exponents so they are the same. Here, we choose to adjust both numbers so they have the highest exponent value.
8.83×10^-2 - 6.01×10^-3
= 8.39×10^-2 - 0.601×10^-2 = (8.39 -0.601)×10^-2 = 7.789×10^-2
Alternatively, you can convert both numbers to standard form and do the subtraction that way.
8.83×10^-2 - 6.01×10^-3
= 0.0883 -0.00601 = 0.07789
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<em>Additional comment</em>
The second attachment shows the relationship between place values and their multiplier in scientific notation.
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The choice of exponent when computing the sum or difference of numbers in scientific notation is usefully informed by an estimate of the value of the sum or difference. A proper choice can avoid the need to adjust the exponent of the result of the operation. Here, we see the subtraction will change the larger value by less than 10%, so the exponent of the result in scientific notation will be that of the larger value (-2).
