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How do you evaluate the limit #(x+3)^1997# as x approaches #-4#?

Answer 1

Emily Ammerman

-1

If x approaches -4

#lim_(x->-4)(x+3)^1997=(-1)^1997#

Even numbers: #(-1)^(2n)=((-1)^2)^n=1^n=1# with n being an Element of #NN#

Uneven numbers: #(-1)^(2n+1)=(-1)^(2n) * (-1)^1=1*(-1)=-1# with n being an Element of #NN#

#1997=998*2+1# #(-1)^1997=-1#

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Answer 2

Charles Anctil

To evaluate the limit of (x+3)^1997 as x approaches -4, we can substitute -4 into the expression. Thus, (-4+3)^1997 simplifies to (-1)^1997. Since 1997 is an odd exponent, (-1)^1997 equals -1. Therefore, the limit of (x+3)^1997 as x approaches -4 is -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.