# How do you find the length of the curve #y=lnabs(secx)# from #0<=x<=pi/4#?

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To find the length of the curve ( y = \ln|\sec(x)| ) from ( 0 \leq x \leq \frac{\pi}{4} ), you can use the arc length formula. The arc length formula for a curve ( y = f(x) ) from ( x = a ) to ( x = b ) is given by:

[ L = \int_a^b \sqrt{1 + \left( f'(x) \right)^2} , dx ]

First, find the derivative ( f'(x) ) of ( y = \ln|\sec(x)| ). Then, substitute ( f'(x) ) into the arc length formula and integrate over the given interval ( 0 \leq x \leq \frac{\pi}{4} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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