limits

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September 22nd 2009, 10:58 PM
samtheman17

limits

Does anyone know how to solve this????

If f(x)=2x−7 find

lim
h→ 0

f(x+h)−f(x)
h
September 22nd 2009, 11:06 PM
Prove It

Quote:

Originally Posted by samtheman17

Does anyone know how to solve this????

If f(x)=2x−7 find

lim
h→ 0

f(x+h)−f(x)
h

$f(x) = 2x - 7$

$f(x + h) = 2(x + h) - 7$

$= 2x + 2h - 7$ .

$f(x + h) - f(x) = 2x + 2h - 7 - (2x - 7)$

$= 2h$ .

So $\frac{f(x + h) - f(x)}{h} = \frac{2h}{h} = 2$ .

Thus

$\lim_{h \to 0}\frac{f(x + h)- f(x)}{h} = \lim_{h \to 0}2 = 2$ .

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