Limit of the form 0/0

  • #1
22
1

Homework Statement

lim x~a 〈√(a⁺2x) -√(3x)〉 ÷ 〈√(3a+x) - 2√x〉[/B]


Homework Equations

rationalisation and factorisation[/B]


The Attempt at a Solution

i had done rationalisation but the form is not simplifying.plzz help me.[/B]
 

Answers and Replies

  • #2
Buzz Bloom
Gold Member
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The attempt at a solution i had done rationalisation but the form is not simplifying.plzz help me.
Hi Victim:

One technique is to take the ratio of the derivatives of the numerator and denominator.

Hope this helps.

Regards,
Buzz
 
  • #3
22
1
Hi Victim:

One technique is to take the ratio of the derivatives of the numerator and denominator.

Hope this helps.

Regards,
Buzz
i need to solve this question without using LH rule,so i had to do it by rationalisation and factorisation.
 
  • #4
Buzz Bloom
Gold Member
2,347
416
rationalisation and factorisation
Hi Victim:

I confess that I do not know this terminology. Many decades ago when I was learning math as an undergraduate, this terminology was not used. I also do not understand the notation: x~a.

You describe the problem as determining a value when x->0, which produces the form 0/0. However, I suggest you recalculate the limit of the denominator as x->0.

Regards,
Buzz
 
  • #5
22
1
Hi Victim:

I confess that I do not know this terminology. Many decades ago when I was learning math as an undergraduate, this terminology was not used. I also do not understand the notation: x~a.

You describe the problem as determining a value when x->0, which produces the form 0/0. However, I suggest you recalculate the limit of the denominator as x->0.

Regards,
Buzz
by x~0 i mean x tends to 0.
rationalising the denominator so that only rational terms are left on the denominator
 
  • #6
Delta2
Homework Helper
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Because the post doesn't show correctly in my browser, are those expressions under square root? Is it
##\lim_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}##
 
  • #7
22
1
Because the post doesn't show correctly in my browser, are those expressions under square root? Is it
##\lim_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}##
yes exactly
 
  • #8
Delta2
Homework Helper
Insights Author
Gold Member
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Ok fine, first multiply both the numerator and the denominator by ##\sqrt{3a+x}+2\sqrt{x}## but do the algebra only in the denominator.

After multiply the fraction that you ll get at the end of the first step, both the numerator and the denominator by ##\sqrt{a+2x}+\sqrt{3x}## but do the algebra only in the numerator.

If all goes well there will be revealed a common factor, which will be simplified and you ll be left with the fraction
##\frac{\sqrt{3a+x}+2\sqrt{x}}{\sqrt{a+2x}+\sqrt{3x}}## which has an easy to find limit.
 
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  • #9
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Ok fine, first multiply both the numerator and the denominator by ##\sqrt{3a+x}+2\sqrt{x}## but do the algebra only in the denominator.

After multiply the fraction that you ll get at the end of the first step, both the numerator and the denominator by ##\sqrt{a+2x}+\sqrt{3x}## but do the algebra only in the numerator.

If all goes well there will be revealed a common factor, which will be simplified and you ll be left with the fraction
##\frac{\sqrt{3a+x}+2\sqrt{x}}{\sqrt{a+2x}+\sqrt{3x}}## which has an easy to find limit.
THANK you so much.you really deserve well !!!
 
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