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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.6 Limits, #2 · Calculus · Limits

(d) If infinitely many …'s are inside every strip around zero then…

Show by example that these statements are false:

(a) If $a_{n} \to L$ and $b_{n} \to L$ then $a_{n} / b_{n} \to 1$

(b) $a_{n} \to L$ if and only if $a_{n}^{2} \to L^{2}$

(c) If $a_{n} < 0$ and $a_{n} \to L$ then $L < 0$

(d) If infinitely many $a_{n}$ 's are inside every strip around zero then $a_{n} \to 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.6 Limits, #2

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