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What is the equation of the tangent line of #f(x)=lnx# at #x=1#?

Answer 1

Ezekiel Alexander

We must first differentiate #f(x)#.

The derivative of #lnx# is #1/x#

The slope of the tangent at a point #x = a# on the function #f(x)# is given by evaluating #f'(a)#.

Hence, the slope of the tangent is #1/1 = 1#.

The function passes through #(1, ln1) = (1, 0)#. Now, we can use point slope form to find the equation of the tangent.

#y - y_1 = m(x - x_1)#

#y - 0 = 1(x - 1)#

#y = x - 1#

Thus, the equation of the tangent is #y = x - 1#.

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Answer 2

Luke Alvarez

The equation of the tangent line of f(x)=lnx at x=1 is y = x - 1.

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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.