1316 (i) Make a guess at the limit (if it exists) by evaluating the function at the
Chapter 1, Problem 13(choose chapter or problem)
(i) Make a guess at the limit (if it exists) by evaluating the function at the specified -values. (ii) Confirm your conclusions about the limit by graphing the function over an appropriate interval. (iii) If you have a CAS, then use it to find the limit. [Note: For the trigonometric functions, be sure to put your calculating and graphing utilities in radian mode.]
(a) \(\lim _{x \rightarrow 1} \frac{x-1}{x^{3}-1} ; x=2,1.5,1.1,1.01,1.001,0,0.5,0.9\),
(b) \(\lim _{x \rightarrow 1^{+}} \frac{x+1}{x^{3}-1} ; x=2,1.5,1.1,1.01,1.001,1.0001\)
(c) \(\lim _{x \rightarrow 1^{-}} \frac{x+1}{x^{3}-1} ; x=0,0.5,0.9,0.99,0.999,0.9999\)
Equation Transcription:
Text Transcription:
lim_x right arrow 1 x-1/x^#-1; x=2,1.5,1.1,1.01,1.001,0,0.5,0.9,
lim_x right arrow 1^+ x-1/x^#-1; x=2,1.5,1.1,1.01,1.001,1.0001
lim_x right arrow 1^- x-1/x^#-1; x=0,0.4,0.9,0.99,0.999,0.9999
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