1
Solution
\(\displaystyle\lim_{x\to -1} \frac{x^9+1}{x^3+1}\)
2
Solution
\(\displaystyle\lim_{x\to 0} \frac{\sin x}{x}\)
3
Solution
\(\displaystyle\lim_{x\to 0} \frac{1-\cos x}{x^2+2x}\)
4
Solution
\(\displaystyle\lim_{x\to 2} \frac{x-2}{x^2-3x+2}\)
5
Solution
\(\displaystyle\lim_{x\to 0} \frac{5x}{\sin^{-1}(x)}\)
6
Solution
\(\displaystyle\lim_{x\to 0} \frac{5^x-1}{5x}\)
7
Solution
\(\displaystyle\lim_{\theta\to\pi/2} \frac{1+\cos(2\theta)}{1-\sin(\theta)}\)
8
Solution
\(\displaystyle\lim_{x\to 0} \frac{x\,3^x}{3^x-1}\)
9
Solution
\(\displaystyle\lim_{x\to\infty} \frac{x^2+5}{e^{2x}}\)
10
Solution
\(\displaystyle\lim_{x\to 0} \frac{x^3}{\sin x - x}\)
Continued
11
Solution
\(\displaystyle\lim_{x\to 0} \frac{x-\tan x}{x^3}\)
12
Solution
\(\displaystyle\lim_{x\to\infty} \frac{(\ln x)^2}{x}\)
13
Solution
\(\displaystyle\lim_{x\to 0^+} x\ln x\)
14
Solution
\(\displaystyle\lim_{x\to\infty} \frac{\ln(5x)}{\sqrt{5x}}\)
15
Solution
\(\displaystyle\lim_{x\to-\infty} x^2 e^{3x}\)
16
Solution
\(\displaystyle\lim_{x\to\infty} x^3 e^{-x^5}\)
17
Solution
\(\displaystyle\lim_{x\to 1} \frac{1+\cos(5\pi x)}{\ln x - x + 1}\)
18
Solution
\(\displaystyle\lim_{x\to\infty} x\sin(5/x)\)
19
Solution
\(\displaystyle\lim_{x\to\infty} x\tan(3/x)\)
20
Solution
\(\displaystyle\lim_{x\to\infty} x^{1/x}\)