help please! Q1) A word problem involving instantaneous velocity that can be solved using limits.the world problem: A football is dropped out of a window of an airplane 4072 feet off theground at a rate of 22t^2 feet per second where t is the amount of time since the footballwas dropped. Find the instantaneous velocity of the ball just before it hits the groundHe said:first find the height function h(t), and then use (h(t2)-h(t1))/(t2-t1) to estimate theinstantaneous velocity, using at least 4 values around the desired time. But i dont know how todo that !please helpQ2a)find a limit with the given properties. Then, justify your answer algebraically.A limit that can be solved by factoring.the Equation: lim x- > positive infinity = (x – 4)/x 2 + 10x + 21).justify the answer algebraically that what i need!

Name: help please! Q1) A word problem involving instantaneous velocity that
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Description: help please! Q1) A word problem involving instantaneous velocity that can be solved using limits.the world problem: A football is dropped out of a window of an airplane 4072 feet off theground at a rate of 22t^2 feet per second where t is the amount

Answered: Q1) A word problem involving…

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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help please!

Q1) A word problem involving instantaneous velocity that can be solved using limits.
the world problem: A football is dropped out of a window of an airplane 4072 feet off the
ground at a rate of 22t^2 feet per second where t is the amount of time since the football
was dropped. Find the instantaneous velocity of the ball just before it hits the ground
He said:first find the height function h(t), and then use (h(t2)-h(t1))/(t2-t1) to estimate the
instantaneous velocity, using at least 4 values around the desired time. But i dont know how to
do that !please help
Q2a)find a limit with the given properties. Then, justify your answer algebraically.
A limit that can be solved by factoring.
the Equation: lim x- > positive infinity = (x – 4)/x 2 + 10x + 21).
justify the answer algebraically that what i need!

Expert Solution

Step 1

(1)

Use the rate of change of velocity to determine the function h(t). Time t is time since the ball was dropped.

$\begin{matrix} \frac{d h}{d t} = 22 t^{2} f t / \sec \\ d h = 22 t^{2} d t \\ \int d h = \int 22 t^{2} d t \\ h = 22 \int t^{2} d t \\ h (t) = \frac{22}{3} t^{3} + C \\ t = 0, h = 0 \\ h (0) = \frac{22}{3} \times 0^{3} + C \\ C = 0 \\ T h u s, h (t) = \frac{22}{3} t^{3} \end{matrix}$

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