- #1
Victim
- 22
- 1
Hi Victim:Victim said:The attempt at a solution i had done rationalisation but the form is not simplifying.pleasez help me.
i need to solve this question without using LH rule,so i had to do it by rationalisation and factorisation.Buzz Bloom said:Hi Victim:
One technique is to take the ratio of the derivatives of the numerator and denominator.
Hope this helps.
Regards,
Buzz
Hi Victim:Victim said:rationalisation and factorisation
by x~0 i mean x tends to 0.Buzz Bloom said: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 exactlyDelta² said: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}}##
THANK you so much.you really deserve well !Delta² said: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.
The "limit of the form 0/0" refers to a mathematical expression in which the numerator and denominator both approach zero as the variable in the expression approaches a certain value. This type of limit is known as an indeterminate form, as it does not have a unique solution.
The limit of the form 0/0 is considered an indeterminate form because it does not have a unique solution. In other words, the value of the limit cannot be determined just by looking at the expression, and further analysis is needed to find the actual value.
No, the limit of the form 0/0 cannot be evaluated by simply plugging in the value of the variable. This is because the expression will result in an undefined value, which does not provide any meaningful information about the limit.
To determine the limit of the form 0/0, you must use mathematical techniques such as factoring, simplifying, or using L'Hôpital's rule. These techniques allow you to manipulate the expression and find the limit in a more precise and meaningful way.
No, the limit of the form 0/0 is not always equal to zero. In fact, the limit can have a variety of values, depending on the specific expression and the mathematical techniques used to evaluate it. It is important to carefully analyze the expression and use appropriate methods to find the actual value of the limit.