Evaluate the limit
Lim f(x+h) – f(x)
h →0 h


when

f(x) = __ 1___
√x


[Read as "the limit as h approaches 0 of the difference quotient {f(x+h)-f(x)}/ h when f(x) equals one over the square root of x."]


no clue how to do this

I'll give you a hint on how to set this up and a trick you may need to solve - then you do the rest and let us know how you do, OK?

When you put the function \frac 1 {sqrt x} into the limit equation, you get this:


\lim_ {h \to 0} \frac {\frac 1 {sqrt {x+h}} - \frac 1 {sqrt x}} h


Massage this a while to geta common denominator -- you'll end up with the difference of two square roots in the numerator. When that happanes a trick that almost always works is to multiply and divide that expression by the sum of the two square roots (i.e. multiply by 1). For example:

\frac { \sqrt a - \sqrt b} c\ =\ \frac {\sqrt a + \sqrt b} c \cdot \frac {\sqrt a - \sqrt b} {\sqrt a - \sqrt b} \ =\ \frac {a - b} {c \sqrt a - c \sqrt b}


Try this and see if it helps.