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How do you find the limit of #1/t - 1/(t^2+t) # as t approaches 0?

Answer 1

Isaiah Allen

#" The Lim."=1#.

The Limit#=lim_(trarr0){1/t-1/(t^2+t)}#

#=lim_(trarr0){1/t-1/(t(t+1))}#

#=lim_(trarr0){(t+1-1)/(t(t+1))}#

#=lim_(trarr0)(cancelt/(cancelt(t+1)))#

#=lim_(trarr0)1/(t+1)#

#=1/(0+1)#.

#:." The Lim."=1#.

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Answer 2

Emilia Aguilar

To find the limit of 1/t - 1/(t^2+t) as t approaches 0, we can simplify the expression first.

Combining the fractions, we get (t - 1)/(t(t+1)).

Next, we can factor the numerator as (t - 1) = -1(1 - t).

Now, we can cancel out the common factor of (t - 1) in the numerator and denominator.

This leaves us with -1/(t+1).

Finally, as t approaches 0, the denominator (t+1) approaches 1.

Therefore, the limit of 1/t - 1/(t^2+t) as t approaches 0 is -1/1, which simplifies to -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.