Compute \(\lim_{x\to 0^+}\,\frac{\left|{x}\right|}{x}\).

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Review the concept: One-sided limits

The left-hand limit uses only values \(x<a\) and the right-hand limit only values \(x>a\). The limit of \(f\) at \(a\) exists if and only if both one-sided limits exist and are equal.

More practice problems: one-sided limits

• ZW-ONE-SIDED-LIMITS-001 For lim _x→ a f(x) to exist it is necessary and sufficient that...
• ZW-ONE-SIDED-LIMITS-002 Compute lim _x→ 0^- (|x|)/(x).
• ZW-ONE-SIDED-LIMITS-004 Compute lim _x→ 2^+ (1)/(x - 2).
• ZW-ONE-SIDED-LIMITS-005 Compute lim _x→ 2^- (1)/(x - 2).
• ZW-ONE-SIDED-LIMITS-006 Compute lim _x→ 0^- (1)/(x^2).
• ZW-ONE-SIDED-LIMITS-007 Compute lim _x→ 1^-(2x+1).
• ZW-ONE-SIDED-LIMITS-008 Let f(x)=x+1 if x<2 and f(x)=x^2-1 if x≥ 2. Compute lim _x→ 2 f(x).
• ZW-ONE-SIDED-LIMITS-009 If lim _x→ a^-f(x)=2 and lim _x→ a^+f(x)=5, does lim _x→ af(x) exist?

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