Calculus: Early Transcendentals, Enhanced Etext
12th Edition
ISBN: 9781119777984
Author: Howard Anton; Irl C. Bivens; Stephen Davis
Publisher: Wiley Global Education US
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Guess the value of the limit (if it exists) by evaluating the function at the given numbers. Report answers accurate to six decimal places. cos(3x) cos(8x) Let f(x) = - x² We want to find the limit lim x->0 cos(3x) - cos(8x) x² Start by calculating the values of the function for the inputs listed in this table. f(x) 0.2 0.1 X 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears lim x-0 cos(3x) cos(8x) x²
Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.)
Let f(x)=cos(9x)−cos(2x)/x^2
We want to find the limit limx→0 cos(9x)−cos(2x)/x^2
Start by calculating the values of the function for the inputs listed in this table.
x
f(x)
0.2
0.1
0.05
0.01
0.001
0.0001
0.00001
Based on the values in this table, it appears limx→0 cos(9x)−cos(2x)/x^2=
a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary.
b. Confirm your estimate in part (a) with a proof.
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