If limx→3f(x)=7, which of the following must be true? I. f is continuous at x = 3 II. f is differentiable at x = 3
1 answer:
Regarding , we cannot ascertain either statement without additional information.
Imagine
In this case, (I) is false since, although the limit exists at and equals 7, we observe
, which indicates that
is not continuous at that point.
(II) is also valid, as is not differentiable at
; specifically,
but
indicating that the derivative is undefined at .
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Answer:
Option 2 50 ≤ s ≤ 100
Option 5 She can make a deposit of $50
Option 6 She can make a deposit of $75
Detailed explanation:
Let
s represent the amount of money Layla puts into her savings account.
We know that
25% = 25/100 = 0.25
50% = 50/100 = 0.50
Thus
----->
----->
The compound inequality is
Check each case
case 1) 25 ≤ s ≤ 50
This statement is falseRefer to the procedurecase 2) 50 ≤ s ≤ 100
This statement is true
Refer to the procedure
case 3) s ≤ 25 or s ≥ 50
This statement is false
Because s ≤ 100 and s ≥ 50
case 4) s ≤ 50 or s ≥ 100
This statement is false
Because s ≤ 100 and s ≥ 50
case 5) She can make a deposit of $50
This statement is true
As the value of s meets the compound inequality
case 6) She can make a deposit of $75
This statement is true
As the value of s meets the compound inequality