for #1 ... rationalize the numerator and simplify to determine the limit.
for #2 ... get a common denominator for the two fractions 1/x and 1/(x+h), combine them, then simplify. might be easier if you view the difference quotient like this ...
I have 2 graded problems that are due monday, september 22.
The directions are to simplify the difference quotients of the following functions:
#1:
f(x) = (√x)
and
#2:
f(x) = 1/x
The difference quotient is: m = (f(x+h) - f(x)) / h
All work/steps must be shown.
I attempted both of the problems but did not get very far. I put the functions into the difference quotient equation but I don't know how to simplify the expressions properly.
#1:
f(x) = (√x)
(√(x+h) - √(x)) / h
#2:
f(x) = 1/x
(((1/(x+h)) - (1/x)) / h
Please respond quickly; all responses are greatly appreciated.