- #1
- 22
- 1
Hi Victim:The attempt at a solution i had done rationalisation but the form is not simplifying.plzz help me.
i need to solve this question without using LH rule,so i had to do it by rationalisation and factorisation.Hi Victim:
One technique is to take the ratio of the derivatives of the numerator and denominator.
Hope this helps.
Regards,
Buzz
Hi Victim:rationalisation and factorisation
by x~0 i mean x tends to 0.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
yes exactlyBecause 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}}##
THANK you so much.you really deserve well !!!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.