What Are One-Sided Limits?
Read this topicExplanations 2
- When we were looking at two-sided limits, we pointed out several examples that did not have limits to better understand what limits were. We promised, however, that one of those…
By Brian Chen
- (Videos) One Sided Limits by PatrickJMT Here's a good video by patrickJMT showing you how to find one sided limits. One sided limits are limits where you either approach a value…
By Alex Federspiel
Problems 13
- Compute the limit limx→0−e1/x\displaystyle \lim_{x \to 0^-} e^{1/x}x→0−lime1/x.
- Let f:R→Rf:\mathbb{R} \to \mathbb{R}f:R→R, fix a∈Ra \in \mathbb{R}a∈R, and assume limx→a+f(x)=∞\lim_{x \to a^+} f(x) = \inftylimx→a+f(x)=∞. Which of the following are true abo…
- Evaluate limx→2+x2−4∣x−2∣\lim_{x\to2^+}{\frac{x^2-4}{|x-2|}}x→2+lim∣x−2∣x2−4
- Evaluate limx→2−x2−4∣x−2∣\lim_{x\to2^-}{\frac{x^2-4}{|x-2|}}x→2−lim∣x−2∣x2−4
- Evaluate limx→−2−{−3xx≤−21−x3−2<x<2(x−3)2−8x≥2\lim_{x\to-2^-}{\begin{cases}-3x&x\leq-2\\1-x^3&-2<x<2\\(x-3)^2-8&x\geq2\end{cases}}x→−2−lim⎩⎨⎧−3x1−x3(x−3)2−8x≤−2−2<x<2x≥2
- Evaluate limx→−2+{−3xx≤−21−x3−2<x<2(x−3)2−8x≥2\lim_{x\to-2^+}{\begin{cases}-3x&x\leq-2\\1-x^3&-2<x<2\\(x-3)^2-8&x\geq2\end{cases}}x→−2+lim⎩⎨⎧−3x1−x3(x−3)2−8x≤−2−2<x<2x≥2
- Evaluate limx→2−{−3xx≤−21−x3−2<x<2(x−3)2−8x≥2\lim_{x\to2^-}{\begin{cases}-3x&x\leq-2\\1-x^3&-2<x<2\\(x-3)^2-8&x\geq2\end{cases}}x→2−lim⎩⎨⎧−3x1−x3(x−3)2−8x≤−2−2<x<2x≥2
- Evaluate limx→2+{−3xx≤−21−x3−2<x<2(x−3)2−8x≥2\lim_{x\to2^+}{\begin{cases}-3x&x\leq-2\\1-x^3&-2<x<2\\(x-3)^2-8&x\geq2\end{cases}}x→2+lim⎩⎨⎧−3x1−x3(x−3)2−8x≤−2−2<x<2x≥2
- Evaluate, limx→0+esinx\lim_{x\rightarrow0^+}e^{\sin{x}}x→0+limesinx
- Evaluate, limx→−1−3x+1\lim_{x\rightarrow-1^-}\sqrt{\frac3{x+1}}x→−1−limx+13
- Using the graph above find limx→3−f(x)\lim\limits_{x\to3^-}f(x)x→3−limf(x)
- Using the given graph, find limx→2+\lim\limits_{x\to2^+}x→2+lim
- Graph the following piece wise function and find limx→1+f(x)\lim\limits_{x\to1^+}f(x)x→1+limf(x) f(x)={x2−4xif1<x<4−2x−2if−3<x≤1f(x)=\begin{cases} x^2-4x \quad \text{if} \quad…