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'***10 points**** Math help?
Evalutate the following limit:
If: f(x)=sin(x+2)
lim x->0 [f(0+x)−f(0)]/0=
please show work. :)
1 Answer
- Tabula RasaLv 69 years agoFavorite Answer
f(x) = sin(x + 2)
As I understand you want to find derivative f'(0) by definition.
f'(0) = lim(h->0) [f(0 + h) - f(0)]/h = lim(h->0) [sin(h + 2) - sin(2)]/h
Apply trigonometric formula
sin(a) - sin(b) = 2 sin((a - b)/2) * cos((a + b)/2)
f'(0) = lim(h->0) 2sin(h/2) * cos((h+4)/2) /h =
= lim(h->0) sin(h/2) * cos((h+4)/2) / (h/2) =
= lim(h->0) [sin(h/2)]/(h/2) * cos((h+4)/2) =
= 1 * cos(2) = cos(2) as lim(x->0) sin(x)/x = 1.
