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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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.



And finally:



which becomes



when you take the limit as

John

My calculator said it, I believe it, that settles it