Rising radiosonde The National Weather Service releases approximately 70,000 radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about 1000 ft/mm until the balloon bursts in the upper atmosphere Suppose a radiosonde is released from a point 6 ft above the ground and that 5 seconds later, it is 83 ft above the ground Let f ( t ) represent the height (in feet) that the radiosonde is above the ground t seconds after it is released. Evaluate f ( 5 ) − f ( 0 ) 5 − 0 and interpret the meaning of this quotient.
Rising radiosonde The National Weather Service releases approximately 70,000 radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about 1000 ft/mm until the balloon bursts in the upper atmosphere Suppose a radiosonde is released from a point 6 ft above the ground and that 5 seconds later, it is 83 ft above the ground Let f ( t ) represent the height (in feet) that the radiosonde is above the ground t seconds after it is released. Evaluate f ( 5 ) − f ( 0 ) 5 − 0 and interpret the meaning of this quotient.
Solution Summary: The author evaluates the difference quotient f(5)-f
Rising radiosonde The National Weather Service releases approximately 70,000 radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about 1000 ft/mm until the balloon bursts in the upper atmosphere Suppose a radiosonde is released from a point 6 ft above the ground and that 5 seconds later, it is 83 ft above the ground Let f(t) represent the height (in feet) that the radiosonde is above the ground t seconds after it is released. Evaluate
f
(
5
)
−
f
(
0
)
5
−
0
and interpret the meaning of this quotient.
4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
Chapter 1 Solutions
Single Variable Calculus Format: Unbound (saleable)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY