If m(x)=1/x+5, when m(1/2)?
1 answer:
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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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Answer:
Lateral surface area of the storage shed = 336 ft²
Step-by-step explanation:
The picture is the complete question.
The shed is in the shape of a rectangular prism. The lateral surface area of the storage shed can be calculated below. The lateral area is the sides of the prism.
lateral area of a rectangular prism = 2h (l + w)
where
l = length
h = height
w = width
h = 8 ft
l = 14 ft
w = 7 ft
lateral area of a rectangular prism = 2h (l + w)
lateral area of a rectangular prism = 2 × 8 × (14 + 7)
lateral area of a rectangular prism = 16 (21)
lateral area of a rectangular prism = 336 ft²
Lateral surface area of the storage shed = 336 ft²
