(a) Graph the function f ( x ) = sin x − 1 1000 sin ( 1000 x ) in the viewing rectangle [ – 2 π , 2 π ] by [– 4, 4 ]. What slope does the graph appear to have at the origin? (b) Zoom in to the viewing window [–0.4, 0.4] by [– 0.25, 0.25] and estimate the value of f' (0). Does this agree with your answer from pan (a)? (c) Now zoom in to the viewing window [– 0.008, 0.008] by [– 0.005, 0.005]. Do you wish to revise your estimate for f' (0)?
(a) Graph the function f ( x ) = sin x − 1 1000 sin ( 1000 x ) in the viewing rectangle [ – 2 π , 2 π ] by [– 4, 4 ]. What slope does the graph appear to have at the origin? (b) Zoom in to the viewing window [–0.4, 0.4] by [– 0.25, 0.25] and estimate the value of f' (0). Does this agree with your answer from pan (a)? (c) Now zoom in to the viewing window [– 0.008, 0.008] by [– 0.005, 0.005]. Do you wish to revise your estimate for f' (0)?
Solution Summary: The author explains that the slope of the graph at the origin appears to be 1. The tangent line at x=0 is approximately joining the points.
(a) Graph the function
f
(
x
)
=
sin
x
−
1
1000
sin
(
1000
x
)
in the viewing rectangle [ – 2π, 2π] by [– 4, 4 ]. What slope does the graph appear to have at the origin?
(b) Zoom in to the viewing window [–0.4, 0.4] by [– 0.25, 0.25] and estimate the value of f'(0). Does this agree with your answer from pan (a)?
(c) Now zoom in to the viewing window [– 0.008, 0.008] by [– 0.005, 0.005]. Do you wish to revise your estimate for f'(0)?
A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.
Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)
use Integration by Parts to derive 12.6.1
Chapter 2 Solutions
Bundle: Calculus: Early Transcendentals, 8th + WebAssign Printed Access Card for Stewart's Calculus: Early Transcendentals, 8th Edition, Multi-Term
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY