text: # What is the limit of (x-cosx/x) as x goes to infinity?
  
  It is $\infty$
  
  #### Explanation:
  
  We have that
  
  ${\lim}_{x \to \infty} \left(x - \cos \frac{x}{x}\right) = {\lim}_{x \to \infty} x - {\lim}_{x \to \infty} \left(\cos \frac{x}{x}\right)$
  
  Hence $- 1 \le \cos x \le 1 \implies - \frac{1}{x} \le \cos \frac{x}{x} \le \frac{1}{x} \implies \left\mid \cos \frac{x}{x} \right\mid \le \frac{1}{x}$
  
  Using the sqeeze theorem we have that
  
  ${\lim}_{x \to \infty} \left(\cos \frac{x}{x}\right) \to 0$ so we have that
  
  lim_(x->oo)(x-cosx/x)=lim_(x->oo) x-lim_(x->oo)(cosx/x)= (oo)-0=oo
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