9. If an object is dropped from a high cliff, then the distance (in feet) traveled after t seconds is given by the function d(t) = 16t?. %3D a. Find the difference quotient (average speed) over the interval [a, a +h]. Include units with your answer. b. Find the limit as h goes to zero of the difference quotient over the interval Ja, a + h|. Include units with your answer. What do you think this limit represent? 10. Given the equation: f(x) = -2x² + 5x – 1, find the equation of a line that passes through %3D a point on the graph where x = -1 and has a slope of -5.
9. If an object is dropped from a high cliff, then the distance (in feet) traveled after t seconds is given by the function d(t) = 16t?. %3D a. Find the difference quotient (average speed) over the interval [a, a +h]. Include units with your answer. b. Find the limit as h goes to zero of the difference quotient over the interval Ja, a + h|. Include units with your answer. What do you think this limit represent? 10. Given the equation: f(x) = -2x² + 5x – 1, find the equation of a line that passes through %3D a point on the graph where x = -1 and has a slope of -5.
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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9a,9b and 10
![# Calculus and Equations: Practice Problems
## Problem 9
If an object is dropped from a high cliff, the distance (in feet) traveled after \( t \) seconds is given by the function \( d(t) = 16t^2 \).
a. **Find the difference quotient (average speed) over the interval \([a, a + h]\). Include units with your answer.**
b. **Find the limit as \( h \) goes to zero of the difference quotient over the interval \([a, a + h]\). Include units with your answer. What do you think this limit represent?**
## Problem 10
Given the equation: \( f(x) = -2x^2 + 5x - 1 \), find the equation of a line that passes through a point on the graph where \( x = -1 \) and has a slope of -5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffccae16d-a3f5-4ed1-bb18-084e96e3fc22%2F221a00e0-7957-4861-bb29-581fad907f17%2Ff3i5ixg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Calculus and Equations: Practice Problems
## Problem 9
If an object is dropped from a high cliff, the distance (in feet) traveled after \( t \) seconds is given by the function \( d(t) = 16t^2 \).
a. **Find the difference quotient (average speed) over the interval \([a, a + h]\). Include units with your answer.**
b. **Find the limit as \( h \) goes to zero of the difference quotient over the interval \([a, a + h]\). Include units with your answer. What do you think this limit represent?**
## Problem 10
Given the equation: \( f(x) = -2x^2 + 5x - 1 \), find the equation of a line that passes through a point on the graph where \( x = -1 \) and has a slope of -5.
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