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Evaluate the Following One Sided Limit: Lim X → 0 − 1 + C O S E C X - Mathematics

Evaluate the following one sided limit:

\[\lim_{x \to 0^-} 1 + cosec x\]

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Solution

\[\lim_{x \to 0^-} \left[ 1 + \cos ec  x \right]\]
\[Let x = 0 - \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ 1 + cosec \left( - h \right) \right]\]
\[ = \lim_{h \to 0} \left[ 1 - cosec h \right] \left[ cosec \left( - \theta \right) = - cosec \theta \right]\]
\[ = 1 - \infty \]
\[ = - \infty\] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 13.11 | Page 11
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