Answer: (a) Given that prove that there exists an open interval containing 0 such that
Chapter 1, Problem 82(choose chapter or problem)
(a) Given that
\(\lim_{x\rightarrow0}\ (3x+1)(3x-1)x^2+0.01=0.01\)
prove that there exists an open interval (a, b) containing 0 such that \((3 x+1)(3 x-1) x^{2}+0.01>0\) for all \(x \neq 0\) in (a, b).
(b) Given that \(\lim_{x\rightarrow c}\ g(x)=L\), where L > 0, prove that there exists an open interval (a, b) containing c such that g(x) > 0 for all \(x \neq c\) in (a, b).
Text Transcription:
lim_x rightarrow 0 (3x + 1)(3x - 1)x^2 + 0.01 = 0.01
(3x + 1)(3x - 1)x^2 + 0.01 > 0
x neq 0
lim_x rightarrow c g(x) = L
x neq c
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