A famous limit

In this video we present a solution to a general limit: (1+a/x)^bx as x approaches infinity.

Thanks for watching I hope you have a great day

Limit of x^x^x as x goes to 0+ :

Limit of (1+1/x)^x as x approaches infinity :

Limit of (x/x+a)^x as x approaches infinity :

Limit of x^x as x goes to 0+ :

I hope you have a great day!

[jibransaleem]

the solution can be even more simplified and can be done by standard limits a standard limit lim xtends to infinity (1+1/x)^x =e or limit x tends to 0 (1+x)^1/x= e so if u multiply and divide a/x and x/a in power the limit doesn't change but then (1+a/x)^x/a becomes e andd the remaining is e^a/x×bx which also equals to e^ab

[sahilharidas]

The video quality is great, but this solution seems very long. You can simply substitute x = at . This will turn the limit into ((1+1/t)^(t))^ab, which will straight away be e^ab using the definition of e.

[bradtramel]

I'm proud of you but I have no idea why I was recommended this

[RishabhSharma]

Neat video. The sound could be louder otherwise awesome!

[chengkaigoh]

Just do a change of variables and bring out exponents and deifnition of e