Questions tagged 'Limits'

• If $f(x) = \begin{cases} x\sin \frac{1}{x},\;\;\;\;\;x \ne 0\\ \;\;\;\;\;\;0,\;\;\;\;\;x = 0 \end{cases}$, then $\underset{x\to 0}{\mathop{\lim }}\,f(x)=$
  Category: fun-lim | Tags: Limits
• $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{x}^{3}}\cot x}{1-\cos x}=$
  Category: fun-lim | Tags: Limits
• $\underset{x\to 0}{\mathop{\lim }}\,\frac{x({{e}^{x}}-1)}{1-\cos x}=$
  Category: fun-lim | Tags: Limits
• $\underset{x\to 1}{\mathop{\lim }}\,\frac{1}{|1-x|}=$
  Category: fun-lim | Tags: Limits
• $\underset{n\to \infty }{\mathop{\lim }}\,\frac{n{{(2n+1)}^{2}}}{(n+2)({{n}^{2}}+3n-1)}=$
  Category: fun-lim | Tags: Limits
• $\underset{n\to \infty }{\mathop{\lim }}\,\frac{\sqrt{n}}{\sqrt{n}+\sqrt{n+1}}=$
  Category: fun-lim | Tags: Limits
• $\underset{x\to a}{\mathop{\lim }}\,\frac{\sqrt{3x-a}-\sqrt{x+a}}{x-a}=$
  Category: fun-lim | Tags: Limits
• If $f(x) = \begin{cases} \,\,\,\,\,\,\,x,\;{\rm{when }}0 \le x \le 1\\ 2 - x,\;{\rm{when }}1 < x \le 2 \end{cases}$, then $\underset{x\to 1}{\mathop{\lim }}\,f(x)=$
  Category: fun-lim | Tags: Limits
• $\underset{x\to 1}{\mathop{\lim }}\,\frac{\log x}{x-1}=$
  Category: fun-lim | Tags: Limits
• If $\underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{n}}-{{2}^{n}}}{x-2}=80$ , where n is a positive integer, then $n=$
  Category: fun-lim | Tags: Limits

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