Question

Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 0 where f of x equals 10 x plus 2 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0

Answer 1

Answer:

Q1: as x approaches 0 from left lim(10x+2)= 2 and as x approaches 0 from right lim(2-x)=2. Therefor, lim as x approaches 0 of f(x)=2

Q2: only one option that makes sense.... as (x-6) can not equal 0, x can not equal 6. Therefore, -inf ; 6

Q3: lim(x+10) as x approaches 8 from left does not equal lim(10-x) as x approaches 8 from right. Hence, limit does not exist.

Q4: lim(-4-x) as x approaches -10 from left = f(-10) = lim(x+16) as x approaches -10 from right = 6. So, answer is lim of f(x) as x approaches -10 = 6

Q5: an example would be (x+1)/((x+1)(x-1)) where (x+1) is removable at x=-1 and (x-1) is non-removable and creates an asymptote at x=1

Step-by-step explanation: