Find the vertical asymptotes (if any) of the graph of the function.(Enter your answers as a comma-separated list.If an answer does not exist, enter DNE ) h(t)=(t^2-5t)/(t^4)-625

Question

Answer 1

To find the vertical asymptotes of the function

, we need to find the values of

for which the denominator is equal to zero, as these are the points where the function is undefined.The denominator of the function is

. To find the values of

for which this expression is equal to zero, we can set it equal to zero and solve for

:

This can be factored as:

Setting each factor equal to zero gives us:

or

Solving these equations gives us:

or

Since we are looking for real values of

, we can ignore the complex solutions. Therefore, the vertical asymptotes of the function

are at

and

.Answer: The vertical asymptotes of the function

are at

and

.

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