Given a function 𝑓(𝑥)= {1-3x+2x^2 if x<0, cosx if 0≥x<π, sin(x/2) if x>π, find the following limits if they exist otherwise write DNE:

Question

a) lim f(x)

x-->0^-

b) lim f(x)

x-->0^+

c) lim f(x)

x-->0

d) lim f(x)

x-->π

Answer 1

Each of the pieces defining f(x) is continuous on the portion of the domain noted for each!

Therefore, a), b) and c) are all 1 and d) is 0