N=2
The smallest value of f(x) on [0, π/2] is 2, which occurs at x = 0. The smallest value of f(x) on [π/2, π] is also 0, which occurs at x = π. So the lower sum is (π/2)(2 + 2) = 2π
The largest value of f(x) on [0, π/2] is 3, which occurs at x = π/2. This is also true for the interval [π/2, π]. So the upper sum is (π/2)(3 + 3) = 3π
n = 4:
f '(x) = cos(x), which is positive for [0, π/2) and negative for (π/2, π]. This tells us that f is an increasing function on [0, π/2) and a decreasing function on (π/2, π]. So for the lower sum you will always evaluate f at the left endpoint of the subinterval if that subinterval lies in [0, π/2], and at the right endpoint of the subinterval if it lies in [π/2, π]
Thus, the lower sum for n = 4 is
(π/4)(f(0) + f(π/4) + f(3π/4) + f(π))
and the upper sum is
(π/4)(f(π/4) + f(π/2) + f(π/2) + f(3π/4)).
the lower sum for n=8 is
(π/8)(f(0)+f(π/8)+f(π/4)+f(3π/8)+f(5π/8...
and the upper sum is
(π/8)(f(π/8)+f(π/4)+f(3π/8)+f(π/2)+f(π/...
Answer:
3⁻⁴
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Exponential Rule [Multiplying]:
Step-by-step explanation:
<u>Step 1: Define</u>
3⁻⁸ × 3⁴
<u>Step 2: Simplify</u>
- Exponential Rule [Multiplying]: 3⁻⁸ ⁺ ⁴
- Combine exponents: 3⁻⁴
Answer:
The edge length of the shipping container is 14 in.
Step-by-step explanation:
The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.
To find the volume of a cube we need to recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. Or as a formula:
where, <em>s</em> is the length of any edge of the cube.
To find the edge length of the shipping container we use the fact that the volume of a cube shaped shipping container is 2744 in³ and the above formula.
(2n / 6n + 4)(3n + 2 / 3n - 28) Given
2n / 2(3n + 2) * 3n + 2 / 3n - 28 Factor out the 2 in the denominator
n / 3n + 2 * 3n + 2 / 3n - 28 Reduce
n * 1 / 3n - 28 Multiply
n / 3n - 28 Multiply
Answer:
n
Hope this helps!
The maximum height of the pumpkin is 3 feet
We have given that,
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.
The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.
We have to determine the maximum height.
<h3>
What is the maxima?</h3>
At the point of maxima f'(x)=0
first, find the maxima
Therefore differentiate the given function with respect to t we get,
h'(t)=0
Then we get,
Therefore the maximum height of the pumpkin is 3 feet.
To learn more about the maxima visit:
brainly.com/question/13995084
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