1. If a rock is thrown upward on the planet Mathemagicland with a velocity of 12 m/s, its height in meters t seconds later is given by y = 12t – 1.86t2. a. Find the average velocity over the given time intervals. i. [1, 2] ii. [1, 1.5] iii. [1, 1.01] iv. [1, 1.001] b. Estimate the instantaneous velocity when t = 1.

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**1.** If a rock is thrown upward on the planet Mathemagicland with a velocity of 12 m/s, its height in meters \( t \) seconds later is given by \( y = 12t - 1.86t^2 \).

a. Find the average velocity over the given time intervals.
   i. \([1, 2]\)
   ii. \([1, 1.5]\)
   iii. \([1, 1.01]\)
   iv. \([1, 1.001]\)

b. Estimate the instantaneous velocity when \( t = 1 \).

**2.** The figure below shows a point \( P \) on the parabola \( y = x^2 \) and the point \( Q \) where the perpendicular bisector of \( QP \) intersects the y-axis. As \( P \) approaches the origin along the parabola, what happens to \( Q \)? Does it have a limiting position? If so, find it.

*Explanation of the Diagram:*

The graph displays a parabola labeled \( y = x^2 \) extending upwards. A point \( P \) is shown on the right arm of the parabola. The perpendicular bisector of line segment \( QP \) is depicted as a dashed line intersecting the y-axis at point \( Q \). As point \( P \) moves closer to the origin along the parabola, the accompanying changes in the position of point \( Q \) are considered for the analysis of its limiting position.
Transcribed Image Text:**1.** If a rock is thrown upward on the planet Mathemagicland with a velocity of 12 m/s, its height in meters \( t \) seconds later is given by \( y = 12t - 1.86t^2 \). a. Find the average velocity over the given time intervals. i. \([1, 2]\) ii. \([1, 1.5]\) iii. \([1, 1.01]\) iv. \([1, 1.001]\) b. Estimate the instantaneous velocity when \( t = 1 \). **2.** The figure below shows a point \( P \) on the parabola \( y = x^2 \) and the point \( Q \) where the perpendicular bisector of \( QP \) intersects the y-axis. As \( P \) approaches the origin along the parabola, what happens to \( Q \)? Does it have a limiting position? If so, find it. *Explanation of the Diagram:* The graph displays a parabola labeled \( y = x^2 \) extending upwards. A point \( P \) is shown on the right arm of the parabola. The perpendicular bisector of line segment \( QP \) is depicted as a dashed line intersecting the y-axis at point \( Q \). As point \( P \) moves closer to the origin along the parabola, the accompanying changes in the position of point \( Q \) are considered for the analysis of its limiting position.
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