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ValdasBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow 0} \frac{ \sqrt[5]{1+2x}1 }{ \sin x }\]
 one year ago

ValdasBest ResponseYou've already chosen the best response.0
sorry, I forgot to mention that we haven't learnt about l`hopital
 one year ago

mykoBest ResponseYou've already chosen the best response.0
you learned Taylors series?
 one year ago

RajshikharGuptaBest ResponseYou've already chosen the best response.1
expand the root term by binomial theorem
 one year ago

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

RajshikharGuptaBest ResponseYou've already chosen the best response.1
while opening with binomial neglect higher degree terms
 one year ago

ValdasBest ResponseYou've already chosen the best response.0
well, 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?
 one year ago

RajshikharGuptaBest ResponseYou've already chosen the best response.1
no see it i have showndw:1353844296253:dw
 one year ago

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

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

RajshikharGuptaBest ResponseYou've already chosen the best response.1
it 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 .....
 one year ago

ValdasBest ResponseYou've already chosen the best response.0
Yes, 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.
 one year ago

RajshikharGuptaBest ResponseYou've already chosen the best response.1
no 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
 one year ago

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

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

pastaBest ResponseYou've already chosen the best response.0
Binomial 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
 one year ago

ValdasBest ResponseYou've already chosen the best response.0
I can't use l'hoptial's rule to find the limit
 one year ago

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

ValdasBest ResponseYou've already chosen the best response.0
We haven't studied about that rule yet
 one year ago

ValdasBest ResponseYou've already chosen the best response.0
This 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
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
@RajshikharGupta 's method seems to be the shortest to me,
 one year ago

pastaBest ResponseYou've already chosen the best response.0
ok ,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
 one year ago

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

ValdasBest ResponseYou've already chosen the best response.0
Yeah, I don't underst that part
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
hmm,,heard of taylor series expansion ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
then 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..
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
make that substitution in your question.. you'll reach the ans directly then..
 one year ago
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