Ineed to find the left-hand, right-hand, and two-sided limits of a few functions (b, c, and d), and b and c are piecewise. i have attached pictures of the functions.

i feel good about my answers to b and c but would like someone to check them. i have an answer for d but am not confident in it because when i graph the original function versus my factored form, it doesn't look the same and i wonder if i factored it incorrectly. there's also a function called a that i am not understanding, but i'm going to leave that for a separate question.

b.
limit from the left = 1/2
limit from the right = sqrt3/2
two-sided limit = dne

c.
limit from the left = sqrt3/2
limit from the right = sqrt3/2
two-sided limit = sqrt3/2, does indeed exist because left and right limits match

d.
i factored this equation as (x + 6) and x can't be 6 (removable discontinuity)
limit from the left = 12
limit from the right = 12
two-sided limit = 12

i put this into the wolfram alpha calculator and got -12 as the left-hand limit. it's more likely that i'm wrong versus the calculator being wrong, so i think i must have factored the original equation improperly or used an improper method for finding the limit.

can someone check my answers to b and c and comment on what i might be doing incorrectly for d?