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What is the equation of the tangent line of #f(x)=cos^3x^2 # at #x=0#?

Answer 1

Luke Alvarez

Hence equation of tangent is y=1

Let #y=cos^3x^2#

Slope of the tangent is

#dy/dx=3cos^2x^2(-sinx^2)(2x)#

#m=-6xcos^2x^2sinx^2#

at x=0

#m=-6xx0xxcos^2 0^2sin0^2#

#m=0#

point of tangency is

#y=cos^3x^2=cos^3 0^2=cos^3 0=(cos0)^2=1^2=1#

Hence equation of tangent is y=1

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Answer 2

Isabella Ackerman

The equation of the tangent line of f(x)=cos^3x^2 at x=0 is y = 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.

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