Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Chapter 1- Rates of Change Lesson 1.2- Rates of Change Using Equations Date: Lesson 1.2 Determining the Average Rate of Change & Instantaneous Rate of Change from an Equation Example 1: A ball is dropped from a cliff that is 125 m high. After t seconds, the ball is s metres above the ground, where s(t)=125-5t³, 0≤rs5. a) Calculate the Average Rate of Change between t=1s and t=3s

Chapter 1- Rates of Change Lesson 1.2- Rates of Change Using Equations Date: Lesson 1.2 Determining the Average Rate of Change & Instantaneous Rate of Change from an Equation Example 1: A ball is dropped from a cliff that is 125 m high. After t seconds, the ball is s metres above the ground, where s(t)=125-5t³, 0≤rs5. a) Calculate the Average Rate of Change between t=1s and t=3s

icon
Related questions
Question

Please help me with this. Please show your worj

Chapter 1 - Rates of Change Lesson 1.2 - Rates of Change Using Equations Date: Lesson 1.2 Determining the Average Rate of Change & Instantaneous Rate of Change from an Equation Example 1: A ball is dropped from a cliff that is 125 m high. After t seconds, the ball is s metres above the ground, where s(t)=125-5t³, 0≤1≤5. a) Calculate the Average Rate of Change between t=1s and t=3s b) Calculate the Average Rate of Change between t=1s and t=1.5s. But if we want to calculate the Instantaneous Rate of Change at 1s what will we do?
Transcribed Image Text:Chapter 1 - Rates of Change Lesson 1.2 - Rates of Change Using Equations Date: Lesson 1.2 Determining the Average Rate of Change & Instantaneous Rate of Change from an Equation Example 1: A ball is dropped from a cliff that is 125 m high. After t seconds, the ball is s metres above the ground, where s(t)=125-5t³, 0≤1≤5. a) Calculate the Average Rate of Change between t=1s and t=3s b) Calculate the Average Rate of Change between t=1s and t=1.5s. But if we want to calculate the Instantaneous Rate of Change at 1s what will we do?
The instantaneous rate of change represents the slope of the tangent to the curve at the point x = a. We have understood from Advanced Functions that the best estimate occurs when the interval used to calculate the rate of change is as small as possible. If we want to know the instantaneous rate of change of f(x) at x = a, consider the intervals between x = a and x = a + h, where h is a really small number that's not 0. The two endpoints of the secant joining these points are: P(a, f(a)) and Q(a+h, f(a+h)). The slope of the secant between P(a, f(a)) and Q(a+h, f(a+h)) is called the Difference Quotient and is calculated as follows: Example 2 Consider the function y=-√2x a) Determine the Average Rate of Change of y with respect to (w.r.t.) x from x=2 to x=8
Transcribed Image Text:The instantaneous rate of change represents the slope of the tangent to the curve at the point x = a. We have understood from Advanced Functions that the best estimate occurs when the interval used to calculate the rate of change is as small as possible. If we want to know the instantaneous rate of change of f(x) at x = a, consider the intervals between x = a and x = a + h, where h is a really small number that's not 0. The two endpoints of the secant joining these points are: P(a, f(a)) and Q(a+h, f(a+h)). The slope of the secant between P(a, f(a)) and Q(a+h, f(a+h)) is called the Difference Quotient and is calculated as follows: Example 2 Consider the function y=-√2x a) Determine the Average Rate of Change of y with respect to (w.r.t.) x from x=2 to x=8
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions