# What is the equation of the tangent line of #f(x) = sec^3x^2# at #x=pi/8#?

At

And the slope is given by

# = 6xsec^3(x^2)tan(x^2)# At

#x = pi/8# , the slope of the tangent line is

#m = f'(pi/8) = 6pi/8sec^3(pi^2/64)tan(pi^2/64)#

# = (3pi)/4sec^3(pi^2/64)tan(pi^2/64)# the equation of the line through

#(pi/8, sec^3(pi^2/64))# with slope#m = (3pi)/4sec^3(pi^2/64)tan(pi^2/64)# is

#y = (3pi)/4sec^3(pi^2/64)tan(pi^2/64)x-(3pi^2)/32sec^3(pi^2/64)tan(pi^2/64)+ sec^3(pi^2/64)#

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The equation of the tangent line of f(x) = sec^3x^2 at x=pi/8 is y = 2√2(x - pi/8) + √2.

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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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