The graph of a functions f(x) is shown as right below. Find the following limits

Question

The graph of a functions f(x) is shown as right below. Find the following limits. If a limit is infinite, state whether it is infinity or -infinity li_x rightarrow (-3) - 1/f(x) lim_x rightarrow 2 f(x) - f(2)/x - 2. Justify your answer. List all values a at which f is continuous but not differentiable. a = List all values b at which f is discontinuous but is continuous from the left. b = f have a removable discontinuity? Circle "YES" or "NO" and answer the question that follow. At what number c? C = What value f(c) will make f continuous at c? f(c) =

Explanation / Answer

a)
Notice at x = -3(-),
which is a value of x slightly less than -3,
the value of y is slightly positive
So, 1/f(x) will be
1/(slightly positive

which is

+infinity

--------------------------------------------------------------

ii)
WE are basically finding f'(2)
which is equal to the slope of the line between
(0,5) and (3,1)

Slope of this line is -4/3

So, f'(2) = -4/3

-4/3 ---> ANSWER

---------------------------------------------------------------

b)
It is cont but not diff at...
a = 0
because at a = 0, the graph has no break
but there is a sharp corner

b = 3

-----------------------------------------------------------------

YES

Yes, it has a removable discontinuity át c = 5

--------------------------------------------------------------

f(c) has to be 2

--------------------------------------------------------------

Yes, jump discon at
x = -2

YES

d = -2

f(d) has to be 3

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.