Answer:
Step-by-step explanation:
The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:
- f(a) is defined.
- The limit of ƒ(x) as x approaches a exists.
- The limit of ƒ(x) as x approaches a is equal to f(a).
(i) Left-hand limit = right-hand limit.
Pass. The limit from either side is 8.
(ii) Left-hand limit = limit.
Pass. If the limits from either direction exist, the limit exists.
(iii) Limit as x ⟶ ∞ is not part of the three-step test.
(iv) Limit as x ⟶ 1 exists. Pass.
(v) f(1) is defined.
FAIL. f(1) is not defined.
(vi) Limit as x ⟶ ∞ is not part of the three-step test.
(vii) Passing the three-step test is not a step in the test.
(viii) The limit as x ⟶ 1 does not equal f(1).
FAIL. f(1) is undefined.
The steps in the three-step test for which the function fails are 
.
Answer:
3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)
(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)
(13,-14) becomes (7 + 13, -14-10) ; (20,-24)
Step-by-step explanation:
What we have to do here is to add 5 to the x-axis value and subtract 12 from the y-axis value
(3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)
(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)
(13,-14) becomes (7 + 13, -14-10) ; (20,-24)
Distance of each track are:
D₁ = 428.5 yd
D₂ = 436.35 yd
D₃ = 444.20 yd
D₄ = 452.05 yd
D₅ = 459.91 yd
D₆ = 467.76 yd
D₇ = 475.61 yd
D₈ = 483.47 yd
<u>Explanation:</u>
Given:
Track is divided into 8 lanes.
The length around each track is the two lengths of the rectangle plus the two lengths of the semi-circle with varying diameters.
Thus,
Starting from the innermost edge with a diameter of 60yd.
Each lane is 10/8 = 1.25yd
So, the diameter increases by 2(1.25) = 2.5 yd each lane going outward.
So, the distances are:
D₁ = 240 + π (60) → 428.5yd
D₂ = 240 + π(60 + 2.5) → 436.35 yd
D₃ = 240 + π(60 + 5) → 444.20 yd
D₄ = 240 + π(60 + 7.5) → 452.05 yd
D₅ = 240 + π(60 + 10) → 459.91 yd
D₆ = 24 + π(60 + 12.5) → 467.76 yd
D₇ = 240 + π(60 + 15) → 475.61 yd
D₈ = 240 + π(60 + 17.5) → 483.47 yd
