SOLUTION: Given the function f(x)=SqRt(x+1) find the difference quotient and simplify.
Now i have found the difference quotient to be [SqRt(x+h+1)-SqRt(x+1)]/h and when i simplify that i
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Question 975670: Given the function f(x)=SqRt(x+1) find the difference quotient and simplify.
Now i have found the difference quotient to be [SqRt(x+h+1)-SqRt(x+1)]/h and when i simplify that i just rearrange the variables so that h is before x.
But im pretty sure that simplifying a difference quotient means rationalizing the numerator in which case i got
h/[h(SqRtx+h+1) + h(SqRtx+1)] or cancel out the h's to get
1/SqRt(x+h+1) + Sqrt(x+1).
But im not sure which one would be correct in the simplified form if the difference quotient is in fact the same as what i got.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Yep, you did it correctly:
When you rationalize the numerator, you end up with the difference of two squares in the numerator and a new factor in the denomiator that is the conjugate of the numerator.
}{h(\sqrt{x\ +\ h\ +\ 1}\ +\ sqrt{x\ +\ 1})})
And finally:
which becomes
when you take the limit as 
John
My calculator said it, I believe it, that settles it
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