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Question Number 93824 by student work last updated on 15/May/20

Answered by john santu last updated on 15/May/20

$$\underset{\mathrm{t}\to 0}{\lim }\mathrm{lny}=\underset{\mathrm{t}\to 0}{\lim }\tan (3\mathrm{t}+\frac{\pi }{2})\ln \left(\tan (\frac{3\mathrm{t}}{2}+\frac{\pi }{4})\right)$$$$=\underset{\mathrm{t}\to 0}{\lim }\frac{\ln \left(\tan (\frac{3\mathrm{t}}{2}+\frac{\pi }{4})\right)}{\cot (3\mathrm{t}+\frac{\pi }{2})}$$$$=\underset{\mathrm{t}\to 0}{\lim }\frac{\ln \left(\tan (\frac{3\mathrm{t}}{2}+\frac{\pi }{4})\right)}{-\tan 3\mathrm{t}}$$$$\mathrm{now}\mathrm{easy}\mathrm{to}\mathrm{solve}$$

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