Question

(x²-x+

X+5 if x 2
Suppose that h(x)= 5
if x=2
*3-1 if x>2
Which of the following is equal to 7?
I. lim hx)
X-2-
II.
lim h(x)
x->2+
III.
lim h(x)
x->2

Answer 1

Sorry to disappoint, but none of these answers are correct. All three limits are equal to 7.

Compute the one-sided limits:

`\displaystyle\lim_(x\to2^-)h(x)=\lim_(x\to2)(x^2-x+5)=2^2-2+5=7`

`\displaystyle\lim_(x\to2^+)h(x)=\lim_(x\to2)(x^3-1)=2^3-1=7`

Both the one-sided limits agree, so the two-sided limit has the same value,

`\displaystyle\lim_(x\to2)h(x)=7`