SOLUTION: evaluate lim h tendin to 0 root of x+h - root x/ h , x is not equal to 0
sir / maam humble requestsolve my problem pls
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Question 642347: evaluate lim h tendin to 0 root of x+h - root x/ h , x is not equal to 0
sir / maam humble requestsolve my problem pls
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The trick here is to deny our instincts and rationalize the numerator
Note that the numerator is the difference of two quantities that we would very much like to square individually. Recalling that the product of a pair of conjugates is the difference of two squares, multiply the fraction by 1 in the form of the conjugate of the numerator divided by itself:
\left(\frac{\sqrt{x\ +\ h}\ +\ \sqrt{x}}{\sqrt{x\ +\ h}\ +\ \sqrt{x}}\right)\ =\ \lim_{x\rightarrow{h}}\,\frac{x\ +\ h\ -\ x}{h\left(\sqrt{x\ +\ h}\ +\ \sqrt{x})}\ =\ \lim_{x\rightarrow{h}}\,\frac{h}{h\left(\sqrt{x\ +\ h}\ +\ \sqrt{x}\right)}\ =\ \lim_{x\rightarrow{h}}\,\frac{1}{\left(\sqrt{x\ +\ h}\ +\ \sqrt{x}\right))
Now all you have to do is drive 
to zero:
John
My calculator said it, I believe it, that settles it
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