Which of the following is false for f(x) = (10x^3-10x^2-10x)/(2x^5-2x)
1 answer:
1) Factor and simplify:
f(x) = [10x (x^2 - x - 1) ] / [ 2x (x^4 - 1) ] =5 (x^2 - x - 1) / (x^4 - 1)
2) Calculate limits
A) limit of f(x) when x -> 0 = 5(-1)/(-1) = 5
=> y-axis is not an asymptote and A is TRUE.
B) Lim of f(x) when x -> +/- ∞ =
5 * (x^2 / x^4 - x / x^4 - 1/ x^4 ) / (x^4 / x^4 - 1 /x^4) = 0 / ∞ = 0
=> x-axis is an asymptote and B is TRUE
C) Lim of f(x) when x -> - 1 =
5 * (x^2 - x - 1) / (x^4 - 1) = 5 * (1 + 1 - 1) / (1 - 1) = 5 / 0 = ∞
=> x = - 1 is an asymptote and C. is FALSE.
Now you have the answer.
If you want you can verify that the last option is TRUE.
I also enclose a picture showing the asymptotes which may help you.
Answer: Option C. is the false one.
f(x) = [10x (x^2 - x - 1) ] / [ 2x (x^4 - 1) ] =5 (x^2 - x - 1) / (x^4 - 1)
2) Calculate limits
A) limit of f(x) when x -> 0 = 5(-1)/(-1) = 5
=> y-axis is not an asymptote and A is TRUE.
B) Lim of f(x) when x -> +/- ∞ =
5 * (x^2 / x^4 - x / x^4 - 1/ x^4 ) / (x^4 / x^4 - 1 /x^4) = 0 / ∞ = 0
=> x-axis is an asymptote and B is TRUE
C) Lim of f(x) when x -> - 1 =
5 * (x^2 - x - 1) / (x^4 - 1) = 5 * (1 + 1 - 1) / (1 - 1) = 5 / 0 = ∞
=> x = - 1 is an asymptote and C. is FALSE.
Now you have the answer.
If you want you can verify that the last option is TRUE.
I also enclose a picture showing the asymptotes which may help you.
Answer: Option C. is the false one.
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Answer:
Step-by-step explanation:
<u>Given information</u>
Point B = (-2, -4)
Reflection line: y = x
<u>Concept:</u>
When reflecting over the line y = x, the position of y and x in the original coordinate switches places.
This is because it is " y = x ", assuming that they could interchange
<u>Find the coordinate of Point B'</u>
Original (x, y) = (-2, -4)
Point B' = (x', y') = (y, x) =
<em>Please refer to the attachment below for a graphical understanding</em>
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