Question

Im really confused in general on part b. im just not sure what to input and where to input it. thanks!

Answer 1

t(i) will be continuous at i = 42,000 if

• the limits of t(i) as i approaches 42,000 from either side both exist, and

• both of these limits agree with the value of t(i) at i = 42,000

By definition of t(i), we have

t (42,000) = 548 + 0.18 (42,000 - 16,000) = 5,228

Now check the one-sided limits - both must have a value of 5,228.

• From the left:

`\displaystyle \lim_(i\to42,000^-)t(i) \\\\ = \lim_(i\to42,000) (548 + 0.18(i-16,000)) \\\\ = 548 + 0.18 \lim_(i\to42,000)(i-16,000) \\\\ =548 + 0.18 (42,000-16,000) \\\\ = 5,228`

• From the right:

`\displaystyle \lim_(i\to42,000^+)t(i) \\\\ = \lim_(i\to42,000)(3,200+b(i-35,000)) \\\\ = 3,200 + b\lim_(i\to42,000)(i-35,000} \\\\ =3,200 + b(42,000-35,000) \\\\ = 3,200-7,000b`

Solve for b :

5,228 = 3,200 - 7,000 b

7,000 b = -2,028

b = -507/1750 ≈ -0.2897