Limits at Infinity
Read this topicExplanations 6
- Sometimes we want to say that a function gets close to some number when xxx gets big. For example, consider the functions f(x)=2−x/3+2f(x) = 2^{-x/3} + 2f(x)=2−x/3+2 and g(x)=x/…
By Samuel Zbarsky, Po-Shen Loh, Mitchell Lee
- Hi. So we've studied the two-sided limits. Now ready for something new? (a.k.a one-sided limits) One-sided limit sometimes means the limit when x→+∞x\rightarrow+\inftyx→+∞ or x→…
By Yuan Yao, Expii Team, Moor Xu
- (Video) Limits to Infinity by A3Academy Limits to Infinity - Introduction First, watch this introduction on Limits to Infinity. Now, answer some questions.
By Aniruddh Iyengar, Alex Federspiel
- We can find the limit by diving the numerator and denominator with x32x^{32}x32 which makes all the terms with x in the denominator to zero, limx→∞x32−3x15+23x32−4x=limx→∞1−3x…
By Vidhya K, Victor Wang, Alex Federspiel
- (Video) Limits at Infinity by PatrickJMT Here's a video by patrickJMT showing you how to find limits of functions as they approach infinity. When we take a limit as it approache…
By Alex Federspiel
- (Video) Calculating a Limit at Infinity with a Radical by PatrickJMT Here's a video by patrickJMT showing you how to find the limit that approaches infinity of rational expressi…
By Alex Federspiel
Problems 12
- Compute limx→∞12x2−3x+24x2+5.\lim_{x \to \infty} \frac{12x^2 - 3x + 2}{4x^2 + 5}.x→∞lim4x2+512x2−3x+2.
- Compute limx→∞x32−3x15+23x32−4x\lim_{x \to \infty} \frac {x^{32}-3x^{15}+2}{3x^{32}-4x}x→∞lim3x32−4xx32−3x15+2
- Let f(x)=2−x+3f(x) = 2^{-x} + 3f(x)=2−x+3. What is limx→∞f(x)\lim_{x \to \infty}f(x)limx→∞f(x)?
- Let f(x)=6x2+53x2+3x+3f(x) = \frac{6x^2 + 5}{3x^2 + 3x + 3}f(x)=3x2+3x+36x2+5. What is limx→∞f(x)\lim_{x \to \infty}f(x)limx→∞f(x)?
- Let f(x)=sin(x)xf(x) = \frac{\sin(x)}{x}f(x)=xsin(x). What is limx→∞f(x)\lim_{x \to \infty}f(x)limx→∞f(x)?
- How does the following function behave for large xxx? f(x)=6x4+2x3−5x−53x4−x3+2x2−x+1f(x) = \frac{6x^4 + 2x^3 - 5x - 5}{3x^4 - x^3 + 2x^2 - x + 1}f(x)=3x4−x3+2x2−x+16x4+2x3−5x−5
- Evaluate limx→∞x2+3x+5x3+6x2−4x+9\lim_{x\to\infty}{\frac{x^2+3x+5}{x^3+6x^2-4x+9}}x→∞limx3+6x2−4x+9x2+3x+5
- Evaluate limx→∞4x4+3x3+2x2+x−12x4+6x3−2x2+5x−7\lim_{x\to\infty}{\frac{4x^4+3x^3+2x^2+x-1}{2x^4+6x^3-2x^2+5x-7}}x→∞lim2x4+6x3−2x2+5x−74x4+3x3+2x2+x−1
- Evaluate limx→∞3x2+6xx4−2x3+10\lim_{x\to\infty}{\frac{3x^2+6x}{\sqrt{x^4-2x^3+10}}}x→∞limx4−2x3+103x2+6x
- Given that e=limx→∞(1+1x)xe=\displaystyle\lim_{x \rightarrow \infty} \left( 1+\frac{1}{x} \right)^xe=x→∞lim(1+x1)x, evaluate limx→0(1+2x)1x.\lim_{x \rightarrow 0} (1+2x)^{\f…
- Evaluate, limx→−∞x2+8x2+9\lim_{x\rightarrow-\infty}\frac{x^2+8}{\sqrt{x^2+9}}x→−∞limx2+9x2+8
- Evaluate, limx→−∞x30−x193x10e+2x5e+3e\lim_{x\rightarrow-\infty}\frac{\sqrt[3]{x^{30}-x^{19}}}{\frac{x^{10}}{e}+\frac{2x^5}{e}+\frac{3}{e}}x→−∞limex10+e2x5+e33x30−x19