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Determine lim x?? f(x) and lim x??? f(x) for the following function. Then give the horizontal asymptotes of f, if any. f(x) = (5x^4 - 1) / (x^5 + 2x^3) Evaluate lim x?? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x?? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.) B. The limit does not exist and is neither ? nor -?. Evaluate lim x??? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x??? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.) B. The limit does not exist and is neither ? nor -?. Identify the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is . (Type equations.) B. The function has one horizontal asymptote, . (Type an equation.) C. The function has no horizontal asymptotes.

          Determine lim x?? f(x) and lim x??? f(x) for the following function. Then give the horizontal asymptotes of f, if any.

f(x) = (5x^4 - 1) / (x^5 + 2x^3)

Evaluate lim x?? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. lim x?? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.)
B. The limit does not exist and is neither ? nor -?.

Evaluate lim x??? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. lim x??? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.)
B. The limit does not exist and is neither ? nor -?.

Identify the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

A. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is . (Type equations.)
B. The function has one horizontal asymptote, . (Type an equation.)
C. The function has no horizontal asymptotes.

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Determine lim x?? f(x) and lim x??? f(x) for the following function. Then give the horizontal asymptotes of f, if any.

f(x) = (5x^4 - 1) / (x^5 + 2x^3)

Evaluate lim x?? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. lim x?? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.)
B. The limit does not exist and is neither ? nor -?.

Evaluate lim x??? f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. lim x??? (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.)
B. The limit does not exist and is neither ? nor -?.

Identify the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

A. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is . (Type equations.)
B. The function has one horizontal asymptote, . (Type an equation.)
C. The function has no horizontal asymptotes.

Added by Kimberly H.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gaurav Kalra

06/02/2022

Step 1

To find the limit as x approaches infinity, we look at the highest degree terms in the function. In this case, the highest degree term is x^5. Therefore, the limit as x approaches infinity of f(x) is infinity. Show more…

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Determine lim x→∞ f(x) and lim x→−∞ f(x) for the following function. Then give the horizontal asymptotes of f, if any. f(x) = (5x^4 - 1) / (x^5 + 2x^3) Evaluate lim x→∞ f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x→∞ (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.) B. The limit does not exist and is neither ∞ nor -∞. Evaluate lim x→−∞ f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x→−∞ (5x^4 - 1) / (x^5 + 2x^3) = (Simplify your answer.) B. The limit does not exist and is neither ∞ nor -∞. Identify the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is (Type equations.) B. The function has one horizontal asymptote, (Type an equation.) C. The function has no horizontal asymptotes.

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00:02 Hi, we're given the function here, affect is equal to, what is given here, apec is equal to 5 x -twe power 4 minus 1, or divide by x2 power 5 plus 2x cube, right? so it's given to us, right? now, the first thing is, let's just solve for here, limit x -10 to infinity apex, right? limit x -10 to infinity apex.

00:40 To solve here, right, this is given as limit x tends to infinity.

00:48 So, fx is 5, xx2 power 4 minus 1 over we have xx2 power 5 plus 2x2.

00:57 Now to solve this, what we do, we factor out the highest power of x, from numerator and denominator.

01:03 So we get here, limit x to infinity.

01:07 So from here, factor out extra power 4, and then this will get here, 5 minus 1 over extra power 4.

01:18 So we get here, whole divided by, here we are now vector out extra power 5 and then we get 1 plus 2 x cubed over extra power 5.

01:32 So we saw this is going to be limit x -10 to infinity and x -tube power 4 over extra power 5.

01:40 That is given as 1 over x .y and let me write this again.

01:48 Will be 1 over x and they will get 5 minus 1 over extra power 4 or divided by x times it will be 1 plus this will give 2 over x square right so we get here now apply the limit here so 1 over infinity that's come out to be 0 this part becomes 0 and this come out of 0 right so we get here will be 1 over infinity let us given as 0 here 0 here 0 times 5 over 1 that is coming out to 0.

02:23 We go to here limit x to infinity fx limit x10 to infinity apex that is coming out to be equal to 0 right and so you can say that for the part the answer is coming out to be 0 all right next term so it's not to be here for a we go with here a basically right we go with a here and the answer is coming out to be 0 the limit is going out to be 0.

02:58 Now, we're on the next one now.

03:00 Limit x tends to minus infinity.

03:03 Limit x tends to minus infinity, all right? we get 5 x2 power 4 minus 1 over we have 50 power 5 plus 2 x cubed...

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