anonymous
  • anonymous
Finding a limit
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \frac{ \sqrt[5]{1+2x}-1 }{ \sin x }\]
anonymous
  • anonymous
try l`hopital
anonymous
  • anonymous
sorry, I forgot to mention that we haven't learnt about l`hopital

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anonymous
  • anonymous
nvm
anonymous
  • anonymous
you learned Taylors series?
anonymous
  • anonymous
Nope
anonymous
  • anonymous
expand the root term by binomial theorem
anonymous
  • anonymous
then there will be term like 10x/sinx and x/sinx=1 for given condition so ans =10
anonymous
  • anonymous
while opening with binomial neglect higher degree terms
anonymous
  • anonymous
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?
anonymous
  • anonymous
no see it i have shown|dw:1353844296253:dw|
anonymous
  • anonymous
and i have done mistake while doing this it is 2/5=0.4 so sorry for that
anonymous
  • anonymous
Could you explain how did you get \[\sqrt[5]{1+2n}=1+\frac{ 2 }{ 5 }n + ....?\]
anonymous
  • anonymous
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 .....
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
Perhaps anyone can think of other way to find the limit? Every problem until this one required some sort of quite simple algebraic manipulation.
anonymous
  • anonymous
actually it is one of the shortest methods but indeed u can initiate in ur problem by factorizing the numerator term
anonymous
  • anonymous
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
anonymous
  • anonymous
I can't use l'hoptial's rule to find the limit
anonymous
  • anonymous
i do not get you.Do you mean ,you are not allowed to use l hopitals rule or you can not evaluate.
anonymous
  • anonymous
We haven't studied about that rule yet
anonymous
  • anonymous
do u want to learn it?
anonymous
  • anonymous
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
shubhamsrg
  • shubhamsrg
@RajshikharGupta 's method seems to be the shortest to me,
anonymous
  • anonymous
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
shubhamsrg
  • shubhamsrg
are you asking how do we get (1+x)^n = 1+xn (given |x|<1 ) ?
anonymous
  • anonymous
Yeah, I don't underst that part
shubhamsrg
  • shubhamsrg
hmm,,heard of taylor series expansion ?
anonymous
  • anonymous
No
shubhamsrg
  • shubhamsrg
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..
shubhamsrg
  • shubhamsrg
make that substitution in your question.. you'll reach the ans directly then..

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