Lim n ightarrow inftyleft(frac4 n^3-74 n^3+3 ight)^sqrtn^5

Transcript

00:01 According to the given quotient limit n tends to infinite 4n cube minus 7 divided by 4n cube plus 3 under root of n raised to power 5.

00:12 So we need to put this value.

00:15 So first of all we need to take n cube as common and this is 4 minus 7 n cube divided by n cube common 4 plus.

00:26 We are going to continue here 4 plus this value would be 4 plus 3 divided by n cube.

00:40 We need to continue here.

00:43 So this is under root of n raised to power 5.

00:47 So limit n tends to infinite.

00:51 This is cancelled out.

00:53 So this is 4 minus 7 divided by infinite cube 4 plus 3 divided by infinite cube under root of infinite raised to power 5.

01:06 So this is 1 raised to power infinity.

01:09 So we need to continue here.

01:11 This value would be we need to take y is equals to or we can say we need to take log of this is log of y is log of.

01:30 We are going to continue here.

01:34 4n cube minus 7 4n cube plus 3.

01:42 This is we need to continue here raised to power under root of n 5.

01:52 So this is limit n tends to infinite.

01:58 So log of y is under root of n raised to power 5 log of 4n minus 7 4n cube plus 3.

02:10 So basically or we can easily one thing we all know if 1 raised to power infinite form this is undetermined form we can easily apply this kind of formula right here.

02:23 This is 1 plus fx raised to power gx.

02:31 This is limit x tends to 0 e raised to power fx gx...

Question

lim _{n ightarrow infty}left(frac{4 n^{3}-7}{4 n^{3}+3} ight)^{sqrt{n^{5}}}

Question

lim _{n ightarrow infty}left(frac{4 n^{3}-7}{4 n^{3}+3} ight)^{sqrt{n^{5}}}

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