Answer:
![\displaystyle y = 45](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%2045)
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]: ![\displaystyle \lim_{x \to c} x = c](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20x%20%3D%20c)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
<em />![\displaystyle y = \lim_{x \to -2} \big[ -3x^3 + 2x^2 - 4x + 5]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%20%5Clim_%7Bx%20%5Cto%20-2%7D%20%5Cbig%5B%20-3x%5E3%20%2B%202x%5E2%20-%204x%20%2B%205%5D)
<u>Step 2: Find Limit</u>
- [Limit] Limit Rule [Variable Direct Substitution]:
![\displaystyle y = -3(-2)^3 + 2(-2)^2 - 4(-2) + 5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%20-3%28-2%29%5E3%20%2B%202%28-2%29%5E2%20-%204%28-2%29%20%2B%205)
- Evaluate:
![\displaystyle y = 45](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%2045)
∴ the limit as <em>x</em> approaches -2 of the given function -3x³ + 2x² - 4x + 5 is equal to 45.
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Learn more about limits: brainly.com/question/26091024
Learn more about calculus: brainly.com/question/26752465
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Answer:4,1x101, 9, 4.1, 2, 0.42, 0.042
Step-by-step explanation:
The hare's final displacement is given by the Pythagorean theorem as
√((13 m)² + (4 m)²) ≈ 13.601 m
The time it took to get there was (31 min)*(60 s/min) = 1860 seconds.
The direction was arctan(4/13) ≈ 17.1° north of east.
The hare's average velocity was (13.601 m)/(1860 s) on a bearing of 72.9°.
0.00731 m/s ∠72.9°
_____
Velocity is a vector quantity having both speed and direction. Here, we choose to express the direction as a bearing measured clockwise from North.
Recall 1πrad = 180°
1 rad = 180/π
so
5π/6 rad = 180/π × 5π /6 = 5×30 = 150.00° (to 2Dp)