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Valdas
 3 years ago
Finding a limit
Valdas
 3 years ago
Finding a limit

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Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 0} \frac{ \sqrt[5]{1+2x}1 }{ \sin x }\]

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, I forgot to mention that we haven't learnt about l`hopital

myko
 3 years ago
Best ResponseYou've already chosen the best response.0you learned Taylors series?

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1expand the root term by binomial theorem

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1then there will be term like 10x/sinx and x/sinx=1 for given condition so ans =10

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1while opening with binomial neglect higher degree terms

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0well, the answer should be 0.4 . And what do you mean by expanding the root term by binomial theorem? Do you mean, that I should raise the fraction by the 5th degree and then use the binomial theorem and numerator?

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1no see it i have showndw:1353844296253:dw

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1and i have done mistake while doing this it is 2/5=0.4 so sorry for that

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0Could you explain how did you get \[\sqrt[5]{1+2n}=1+\frac{ 2 }{ 5 }n + ....?\]

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1it is binomial theorem u will learn this in algebra in high school it is (1+x)^n=1+(nC1)x+(nC2)x^2+(nC3)x^3 and so on .....

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, I know the binomial theorem, but how does it apply to roots? I thought that the power of polynomial it is raised to must be an integer to apply this theorem.

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1no it can be applied on roots if x is very small and it can even for any fractional powers for same case it quite valid approximation tool in maths and physics u can conform it with ur teachers

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0Perhaps anyone can think of other way to find the limit? Every problem until this one required some sort of quite simple algebraic manipulation.

RajshikharGupta
 3 years ago
Best ResponseYou've already chosen the best response.1actually it is one of the shortest methods but indeed u can initiate in ur problem by factorizing the numerator term

pasta
 3 years ago
Best ResponseYou've already chosen the best response.0Binomial theorem just makes work hard ,learn l hopitals rule it is easy.LOOK IF after substituting the limit you get 0/0 differentiate the numenartor and denominator independently the find the limit three steps

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0I can't use l'hoptial's rule to find the limit

pasta
 3 years ago
Best ResponseYou've already chosen the best response.0i do not get you.Do you mean ,you are not allowed to use l hopitals rule or you can not evaluate.

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0We haven't studied about that rule yet

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0This problem can be solved without use of l'hopitals rule, I want to find out how. Perhaps there is some simple algebraic trick which could be used to find the limit or something like that

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0@RajshikharGupta 's method seems to be the shortest to me,

pasta
 3 years ago
Best ResponseYou've already chosen the best response.0ok ,I SEE.I have two solutions so far ,binomial and l'hopitals.But looks like there are one's and may be try following the trigonometry side or otherwise am still checking

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0are you asking how do we get (1+x)^n = 1+xn (given x<1 ) ?

Valdas
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah, I don't underst that part

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0hmm,,heard of taylor series expansion ?

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0then you might just wanna mug up this formulla : dw:1353848320044:dw you'll get to know how we get this when you learn taylor series..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0make that substitution in your question.. you'll reach the ans directly then..
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