One key concept to know in these types of question is the general formula of LRAM (left rectangle approximation), MRAM (midpoint rectangle approximation), and RRAM (right rectangle approximation).
Assuming there are N rectangles, on the interval [a, b] in a function f(x), these would be the "general formulas".
i) RRAM:
ii) LRAM:
iii) MRAM:
Knowing these general formulas, we can figure out these 4 questions.
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Question 11:
Looking at the problem, the sigma notation has the general formula of the RRAM. a = 0, (b-a) = 1, f(x) = x^4, N = infinity.
Hence, we can describe this area represented by the limits as the right rectangle approximation of f(x) = x^4 in the interval of [0, 1] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = x^4 in the interval of [0, 1].
Question 12:
Looking at the problem, the sigma notation has the general formula of the RRAM. a = 2, (b-a) = 3, f(x) = x^4, N = infinity.
Hence, we can describe this area represented by the limits as the right rectangle approximation of f(x) = x^4 in the interval of [2, 5] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = x^4 in the interval of [2, 5].
Question 13:
Looking at the problem, the sigma notation has the general formula of the LRAM. a = -2, (b-a) = 5, f(x) = e^x, N = infinity.
Hence, we can describe this area represented by the limits as the left rectangle approximation of f(x) = e^x in the interval of [-2, 3] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = e^x in the interval of [-2, 3].
Question 14:
Looking at the problem, the sigma notation has the general formula of the MRAM. a = pi/3, (b-a) = pi/2, f(x) = sin(x), N = infinity.
Hence, we can describe this area represented by the limits as the mindpoint rectangle approximation of f(x) = sin(x) in the interval of [pi/3, 5pi/6] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = sin(x) in the interval of [pi/3, 5pi/6].
Hi,
Thank you for your question.
One key concept to know in these types of question is the general formula of LRAM (left rectangle approximation), MRAM (midpoint rectangle approximation), and RRAM (right rectangle approximation).
Assuming there are N rectangles, on the interval [a, b] in a function f(x), these would be the "general formulas".
i) RRAM:
ii) LRAM:
iii) MRAM:
Knowing these general formulas, we can figure out these 4 questions.
Question 11:
Looking at the problem, the sigma notation has the general formula of the RRAM. a = 0, (b-a) = 1, f(x) = x^4, N = infinity.
Hence, we can describe this area represented by the limits as the right rectangle approximation of f(x) = x^4 in the interval of [0, 1] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = x^4 in the interval of [0, 1].
Question 12:
Looking at the problem, the sigma notation has the general formula of the RRAM. a = 2, (b-a) = 3, f(x) = x^4, N = infinity.
Hence, we can describe this area represented by the limits as the right rectangle approximation of f(x) = x^4 in the interval of [2, 5] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = x^4 in the interval of [2, 5].
Question 13:
Looking at the problem, the sigma notation has the general formula of the LRAM. a = -2, (b-a) = 5, f(x) = e^x, N = infinity.
Hence, we can describe this area represented by the limits as the left rectangle approximation of f(x) = e^x in the interval of [-2, 3] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = e^x in the interval of [-2, 3].
Question 14:
Looking at the problem, the sigma notation has the general formula of the MRAM. a = pi/3, (b-a) = pi/2, f(x) = sin(x), N = infinity.
Hence, we can describe this area represented by the limits as the mindpoint rectangle approximation of f(x) = sin(x) in the interval of [pi/3, 5pi/6] using infinite rectangles.
As there are infinite rectangles and the approximation would be very close (considerably equal) to the area underneath, another way you could describe this area is the area underneath the function f(x) = sin(x) in the interval of [pi/3, 5pi/6].
Does this answer your question?