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How do you evaluate the limit #cos((pix)/3)# as x approaches #2#?

Answer 1

Scarlett Allison

#lim_(xrarr2) cos((pix)/3)=cos((2pi)/3)=-0.5#

Since #cos((pix)/3)# is defined when #x=2#

The limit as #xrarr2# of #cos((pix)/3)# is #cos((pi2)/3)# which is one of the "standard" trigonometric angles.

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Answer 2

Isabella Ackerman

To evaluate the limit of cos((πx)/3) as x approaches 2, we substitute the value of x into the function.

cos((πx)/3) = cos((π(2))/3) = cos((2π)/3)

The value of cos((2π)/3) is -1/2.

Therefore, the limit of cos((πx)/3) as x approaches 2 is -1/2.

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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.