limit as theta -> 0 of sin(theta)/ theta + tan(theta)
@Djordje:thanks for contribution but you’re wrong, bro!
Ok Rebeca, what you need to do is to divide both of the numerator and the denominator by Sin(theta).
By doing this, the numerator is 1 and the bottom is [(theta/sin(theta))+(1/cos(theta))].
We have lim(x->0) of (sin x)/x =1 thus lim(theta->0) of (theta/sin(theta)) = lim(theta->0) of [sin(theta)/theta]^-1
= [lim(theta->0) of sin(theta)/theta ]^-1 = 1^-1 =1.
And, of course, lim (theta->0) of 1/cos(theta) =1 when we plug theta=0 in cos(theta)
Therefore, the LIMIT = 1/(1+1) = 1/2.