**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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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.

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

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

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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Question

**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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