Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same info
1 answer:
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Step-by-step explanation:
Q3
(a) If 0 < |x − 1| < δ, then |f(x) − 2| < 2
What this means is, how far can x stray from the x=1 line such that f(x) stays within 2 units of the y=2 line (0 < f(x) < 4).
If we move 2 units left of x=1, we get f(x) = 4.
If we move about 3.5 units right of x=1, we get f(x) = 4.
Therefore, δ can't be more than 2.
(b) If 0 < |x| < δ, then |f(x) − 3| < 1
What this means is, how far can x stray from the x=0 line such that f(x) stays within 1 unit of the y=3 line (2 < f(x) < 4).
If we move 1 unit left of x=0, we get f(x) = 4.
If we move 1 unts right of x=0, we get f(x) = 2.
Therefore, δ can't be more than 1.
Since f(x) isn't continuous within this domain, we can't conclude that the limit exists.
Q4
(a) Yes. If δ = 0.25, then 0.75 < x < 1.25, and f(x) > 200.
(b) No. f(1) = 300, so even if δ = 0, f(x) will be less than 400.
(c) Yes. If δ ≈ 0.1, then 0.9 < x < 1, and f(x) > 450.
Answer:
The limit of the function does not exists.
Step-by-step explanation:
From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.
For x<2
The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.
For x>2
The value of y is 1 at x=2, because of he close circles on (2,1).
For x=2
Therefore the graph represents a piecewise function, which is defined as
The limit of a function exist at a point a if the left hand limit and right hand limit are equal.
The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.
Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.