f(2+h) = |2+h-5|-7 = |h-3| -7
as h---> 0 this is 3-h-7 = -h -4
f(2) = |-3| -7 = 3-7 = -4
so
[ -h - 4 + 4 ] /h
= h/h
= 1
Find lim h->0 [f(2+h)-f(2)]/h where f(x)=|x-5|-7
3 answers
At x=2, x-5 < 0, so the slope at x=2 is just -1.
Ok, ok, algebraically,
f(2+h) = |2+h-5|-7 = |-3+h|-7
Since the value is negative, that will be 3-h-7 = -4-h
f(2) = |2-5|-7 = 3-7 = -4
-4-h - (-4) = -h
Now, divide by h and you have -h/h = -1
Ok, ok, algebraically,
f(2+h) = |2+h-5|-7 = |-3+h|-7
Since the value is negative, that will be 3-h-7 = -4-h
f(2) = |2-5|-7 = 3-7 = -4
-4-h - (-4) = -h
Now, divide by h and you have -h/h = -1
-h/h
or
-1
or
-1
1 answer