L'Hospital's Rule for tan(x) and tan(10x) at 9pi/4: Exact Value Calculation

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The forum discussion focuses on calculating the limit of (tan(x))^tan(10x) as x approaches 9π/4 using L'Hospital's Rule. The initial approach involves taking the natural logarithm of the function, leading to the expression ln(y) = tan(10x) * lim(ln(tan(x))). A key correction is highlighted, where the user is advised to retain tan(10x) in the limit and convert it to cot(10x) for proper application of L'Hospital's Rule. The final step requires exponentiation to obtain the exact value.

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lim (x approaches 9pi/4) (tanx)^tan10x

use L'Hospital's Rule to find the exact valuemy attempt:
y = lim (tanx)^tan10x
lny= lim ln(tanx)^tan10x
= tan10x lim ln(tanx)

I really don't know where to go from there

-Thanks
 
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In your last line, you take tan10x out of the limit without evaluating it. Put it back in and turn it into cot(10x) to put it on the bottom, then apply L'Hospital's. Make sure to apply exp at the end to get the final answer.
 

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