tristensandall13 tristensandall13
  • 24-03-2021
  • Mathematics
contestada

(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

xx X5 if x 2 Suppose that hx 5 if x2 31 if xgt2 Which of the following is equal to 7 I lim hx X2 II lim hx xgt2 III lim hx xgt2 class=

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LammettHash
LammettHash LammettHash
  • 24-03-2021

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

Compute the one-sided limits:

[tex]\displaystyle\lim_{x\to2^-}h(x)=\lim_{x\to2}(x^2-x+5)=2^2-2+5=7[/tex]

[tex]\displaystyle\lim_{x\to2^+}h(x)=\lim_{x\to2}(x^3-1)=2^3-1=7[/tex]

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

[tex]\displaystyle\lim_{x\to2}h(x)=7[/tex]

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