Infinite Limits
Read this topicExplanations 2
- It's easy for a limit to be equal to infinity. For example, what is the limit of 1x\frac{1}{x}x1 as xxx approaches 0 from the positive side? Clearly 11,10.1,10.00001,...\frac{1…
By Vincent Huang, Moor Xu
- (Video) Infinite Limits by PatrickJMT Here's a video by patrickJMT showing you how to find the limit when it equals infinity.
By Alex Federspiel
Problems 13
- Compute limx→−7−3x+7.\lim_{x \to -7^-} \frac {3} {x+7}.x→−7−limx+73.
- Evaluate the following limit. limx→1−1x−1\lim_{x \to 1^-} \frac {1}{x-1}x→1−limx−11
- Fix a∈Ra \in \mathbb{R}a∈R and a real-valued function fff. If limx→a−f(x)=∞\lim_{x \to a^-}f(x) = \inftylimx→a−f(x)=∞, then what is f(a)f(a)f(a)?
- 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…
- Find limx→3x2−x−12x−3\lim_{x\to3}{\dfrac{x^2-x-12}{x-3}}x→3limx−3x2−x−12
- Find limx→−1cos(x)(x−1)xex\lim_{x\to-1}{\cos(x)(x-1)\sqrt{x}e^x}x→−1limcos(x)(x−1)xex
- Find limx→2ln(x)(x−2)2\lim_{x\to2}{\frac{\ln(x)}{(x-2)^2}}x→2lim(x−2)2ln(x)
- Evaluate limx→3+x−1x−3\lim_{x\to3^+}{\frac{x-1}{x-3}}x→3+limx−3x−1
- Evaluate limx→3+x−1x2−7x+12\lim_{x\to3^+}{\frac{x-1}{x^2-7x+12}}x→3+limx2−7x+12x−1
- True or False\text{True or False}True or False === If a>0a>0a>0 then limx→a+xx+a=∞\lim_{x\to a^+}{\dfrac{x}{x+a}}=\inftylimx→a+x+ax=∞
- What values of aaa satisfy limx→ax−3x2−4x−5=∞\lim_{x\to a}{\dfrac{x-3}{x^2-4x-5}}=\inftylimx→ax2−4x−5x−3=∞
- Find aaa limx→ax+8x2−16x+64=∞\lim_{x\to a}{\frac{x+8}{x^2-16x+64}}=\inftyx→alimx2−16x+64x+8=∞
- Evaluate the following expression: limx→2x−2x2−4\lim_{x \to 2} \frac{x-2}{x^2-4}limx→2x2−4x−2