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Answer:
The remainder is 55
Step-by-step explanation:
Let
According to the remainder theorem, if p(x) is divided by x+a, the remainder is p (-a).
The given divisor is x+2, therefore the remainder is given by:
We substitute x=-2 to get:
We simplify to obtain:
We multiply to get:
Therefore the remainder is 55
Answer:
y = 20
Step-by-step explanation:
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
<h3>How to determine which statement is true?</h3>To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
<h3>Conditions for continuity and differentiablity of a function.</h3>
- For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is
. So,
must exist since
- Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
Learn more about continuity of a function here:
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