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can someone help my find the limit if x>0 sinx/ cubed root of x
 one year ago
 one year ago
can someone help my find the limit if x>0 sinx/ cubed root of x
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.1
multiply and divide by x , to get the function in the form of sin x/ x
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
can u draw it out so i can see what ur talking about
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\huge\frac{sin x}{x}\:\frac{x}{\sqrt[3]{x}}\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
and then from there which method would u use
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
u know the formula : \[\lim_{x \rightarrow 0}\: sinx / x = 1\] ? use that for first fraction.
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! omg now it makes sense thank you @hartnn
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
welcome :) what did u get the final answer as ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yup, its 0 good work :)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
i need help again actually with number 84 now
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
ok, if f(x) = root x what will be f(x+h) ?? u know?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
im confused on tht part
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
ok, to get f(x+h) just replace x by (x+h) in f(x) so f(x+h) will be \(\sqrt{x+h}\) ok?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i m using h instead of delta x just for convenience here. so now u put that in {f(x+h)f(x) }/ h to get \(\frac{\sqrt{x+h}\sqrt{h}}{h}\) got this ?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
yeah i got tht part
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
now mutiply and divide by \(\sqrt{x+h}+\sqrt{h}\) and use (a+b)(ab) = a^2  b^2 and tell me what u get in numerator ?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh so ur multiplying it by its conjugate right ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yup, so that i get only h in numerator and that i can cancel it with h in denominator ok?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i made a typo ..... it should be \(\sqrt{x} \) and not \(\sqrt{h} \) in the numerator
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
wait a minute now im confused a bit
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
because itsf(x+h)  f(x) which is \(\sqrt{x+h} \) \(\sqrt{x} \)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so now now mutiply and divide by \(\sqrt{x+h}+\sqrt{x}\) and use (a+b)(ab) = a^2  b^2 and tell me what u get in numerator ?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
would it still be h in the numerator i think..
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yup, because (x+h) x = x+hx = h this h cancels out with h in denominator and u have only 1 in numerator, right ? and what u have in denominator now?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
do you have \[\sqrt{x+h} + \sqrt{x}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes, u are right, be confident :) now just put h =0 because lim h> 0 and tell me what u get in denominator after putting h=0
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
\[\sqrt{x+0} +\sqrt{x}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yup, thats your denominator = \(2\sqrt{x}\) and then your final answer would be \(\huge\frac{1}{2\sqrt{x}}\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
hang on im confused how do u get \[\frac{ 1 }{ 2\sqrt{x} }\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\sqrt{x+0} +\sqrt{x}=\sqrt{x} +\sqrt{x}=2\sqrt{x}\) and there was 1 in the numerator, previously, right ?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
u r a very helpful math teacher!
 one year ago
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