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How do I compute a tan limit with a fraction?

$$\lim_{h\rightarrow 0}\frac{\tan(-\frac{\pi}{4})+1}{h}$$

  • 3
    Do you know what $\tan -\frac{\pi }{4}$ is?2012-06-25
  • 0
    Its -1 i assume? or 0 ?2012-06-25
  • 8
    Don't assume. It's a basic value, so you should know it.2012-06-25
  • 0
    And if you don't know it, you should be able to work it out.2012-06-25
  • 0
    You should at first learn about [trigonometric functions](http://en.wikipedia.org/wiki/Trigonometric_functions) before calculus.2012-06-25
  • 0
    Was this really the question, or was it $\lim_{h\rightarrow 0}\frac{\tan(-\frac{\pi}{4}+h)+1}{h}$?2012-06-25

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Since $ \tan(- \pi /4 ) + 1 = 0$, we have

$$ \lim_{h \rightarrow 0} \frac{\tan \left ( \frac{- \pi}{4} \right ) + 1}{h} = \lim_{h \rightarrow 0} \frac{0}{h} = \lim_{x \rightarrow 0} 0 = 0 $$