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What is the equation of the tangent line of #f(x) =sqrt(ln(cosx))# at # x = pi/4#?

Answer 1

This function does not exist anywhere. There is no tangent line.

For the function #y=cosx#, its range is #-1lt=ylt=1#. These values are then plugged into #ln(x)#. For #0ltxlt=1#, we see that #ln(x)<0#. At #x<0#, #ln(x)# is undefined.

So for this function, we have #sqrtx# when #x<0#, which does not exist. This is an impossible function unless it looked like #sqrtabs(ln(abscos(x)))#.

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Answer 2

Christopher Allers

The equation of the tangent line of f(x) = sqrt(ln(cosx)) at x = pi/4 is y = -sqrt(2) + sqrt(2)(x - pi/4).

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Answer from HIX Tutor

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.