limits: [sin(x+h)-sinx]/h and (2x+sin2x)/x

[ashley123456789]

1) lim ....sin(x+h)-sinx is
... h->0 ........ h

2) lim ......2x+sin2x =
... x->0 ......... x

i have no idea..any help would be great.thanks

 

[Deleted member 4993]

Re: limits

the lim ....sin(x+h)-sinx is
... h->0 ........ h

One of the method would be to expand sin(x+h) and use lim(h ->0) sin(h)/h = 1. Remember that the limit in question is the definition of the derivative of sin(x)


lim ......2x+sin2x =
x->0 ......... x

hint: use

lim (x ->a)[f(x) + g(x)] = lim (x ->a)[f(x)] + lim (x ->a)[g(x)]

also

lim(h ->0) sin(h)/h = 1
i have no idea..any help would be great.thanks