1,134 Answered Questions for the topic AP Calculus
Project: Designing a Roller Coaster - AP Calculus
Project: Explain the mathematics of roller coaster construction. Imagine you are a roller coaster designer, and are asked to mathematically represent the curve of the first drop of a new ride. By...
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01/23/20
Evaluate given equation
Use your calculator to evaluate . Give your answer to the nearest integer. (4 points)
01/23/20
Write the Riemann sum to find the area under the graph of the function f(x) = x^4 from x = 5 to x = 7.
Question options:
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01/23/20
Write the integral that has the same value as the limit
The Riemann sum, , is equivalent to with .Write the integral that produces the same value as . Question options:
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2)
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4)
01/23/20
If the area under the curve of f(x) = 25 - x^2 from x = -4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?
Question options:
1)
Underestimate
2)
Overestimate
3)
The area will be exact
4)
The area cannot be estimated with just four rectangles
01/23/20
Write the summation to estimate the area under the curve y = 2x^2 + 1 from x = 0 to x = 4 using 4 rectangles and left endpoints.
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01/23/20
List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.
Question options:
1)
2, 4, 6, 8, 10
2)
1, 3, 5, 7, 9
3)
0, 2, 4, 6, 8
4)
1, 2, 3, 4, 5
01/22/20
Is the function True or False
Which of the following is true for ?Question options:
1)
There is a removable discontinuity at x = 3.
2)
There is a non-removable discontinuity at x = 3.
3)
The function is continuous for...
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01/22/20
List discontinuities for function
List the discontinuities for the function f(x) = cot( ). Question options:
1)
n( ), where n is an integer
2)
n( ), where n is an integer
3)
n( ), where n is an integer
4)
There are...
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01/22/20
Find where equation is discontinuous
Where is discontinuous? Question options:
1)
f(x) is continuous everywhere
2)
1
3)
1, 4
4)
4
01/22/20
Find value where f(x) is continuous everywhere
To two decimal places, find the value of k that will make the function f(x) continuous everywhere. Question options:
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1.88
2)
9.00
3)
3.76
4)
None of these
01/22/20
Find limit using direct substitution
Find the limit of the function by using direct substitution.Question options:
1)
Does not exist
2)
−6
3)
6
4)
0
01/22/20
Find lim x --> 1 f(x) using graph
Using the graph of f(x) below, find .Question options:
1)
2
2)
−1
3)
−2
4)
Does not exist
01/20/20
Volume of Cylinder
The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units...
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01/20/20
Find Maximum Volume
A 160-inch strip of metal 20 inches wide is to be made into a small open trough by bending up two sides on the long side, at right angles to the base. The sides will be the same height, x. If the...
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01/18/20
Find maximum volume
A 160-inch strip of metal 20 inches wide is to be made into a small open trough by bending up two sides on the long side, at right angles to the base. The sides will be the same height, x. If the...
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