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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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e42e738-88cb-4b54-bc59-c9d4993b7282%2F2c0df5ed-dd87-48c1-b3a2-a3ffb94b2de5%2Fo8d97nn_processed.jpeg&w=3840&q=75)
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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