25,270 Answered Questions for the topic calculus

Calculus Math

11/10/23

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 500 cubic centimeters of soup. The s...
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 500 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing... more
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Calculus Math

11/10/23

Find the point or points on the curve y^2 - 4 x^2 = 70 that is closest to ( 5 , 0 )
Applied OptimizationFind the point or points on the curve y2 - 4x2 = 70 that is closest to ( 5 , 0 ).The point is _____ (enter your answer as an ordered pair; if there is more than one answer,... more
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Calculus Math Physics

11/10/23

Calculus I Anti-derivatives Question A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming that the air resistance can be ignored, how high does it go?
A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint:The acceleration due to... more
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Calculus Math

11/10/23

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 - x^2 . What are the dimensions of such a rectangle with the greatest possible area?
Applied OptimizationA rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 - x2. What are the dimensions of such a rectangle with the greatest possible... more
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Calculus Math

11/10/23

If 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Applied OptimizationIf 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.Volume = _____ cubic centimeters
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Calculus Math Geometry

11/10/23

Calculus I Applied Optimization Problem- How many trees should a farmer plant per acre to maximize her harvest?
A farmer finds that if she plants 90 trees per acre, each tree will yield 25 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by... more
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Calculus Math Geometry

11/10/23

If 2200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
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11/10/23

Calculus I Applied Optimization Problem (Objective: Find the dimensions for the package that will minimize production cost.)
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing... more
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11/10/23

Related Rates Problem (Analytical Geometry & Calculus I)- Goal: Find the rate of change of the area enclosed between the circle and the square
A circle is inside a square.The radius of the circle is increasing at a rate of 3 meters per hour and the sides of the square are increasing at a rate of 1 meter per hour.When the radius is 6... more
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Calculus Math Geometry

11/10/23

Calculus I Related Rates Problem (An inverted pyramid is being filled with water at a constant rate)
An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is... more
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11/10/23

Calculus I Related Rates (Distance between two sailing ships)
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing... more
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11/10/23

Analytical Geometry Question! (Calculus I Trigonometry & Related Rates)
Given:A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the... more
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11/10/23

Calculus I Related Rates Problem! (Differential Equations)
A police car is located 70 feet to the side of a straight road.A red car is driving along the road in the direction of the police car and is 110 feet up the road from the location of the police... more
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Calculus

11/10/23

Find the general indefinite integral
∫(sin2x)/(sinx)dx
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Calculus

11/10/23

Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0,1]
limn→∞∑ni=1(i4/n5+i/n2)I got Δx=1/n and xi=i/n but I'm not sure how else to proceed by the Riemann sum method.
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Calculus

11/10/23

Evaluate the integral by interpreting it in terms of areas
∫(x-√(25-x2)dx, on the integral, [5,-5]
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Calculus

11/10/23

Linear Approximation
Use linear approximation, i.e. the tangent line, to approximate 1.003 as follows: Let f(x) = ‡ and find the equation of the tangent line to f(x) at a "nice" point near 1.003, f(1.003)). Then use... more
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11/10/23

The diagram below consists of a semicircle with center Z and squares LIKE, MORE, and MATH. If the area of square LIKE is 100, what is the area of square MATH? Your answer must be exact. Show work

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Calculus Precalculus

11/09/23

A farmer builds a rectangular grid of pens with 1 row and 5 columns using 850 feet of fencing. What dimensions will maximize the total area of the pen?

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Calculus

11/09/23

This is a series that I could use some help with solving. Could I get some help solving this series please? Thanks much!!!
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Calculus

11/09/23

This is a series that I could use some help with solving. Could I get some help solving this series please? Thanks much!!!
b. How many terms are needed to approximate this series to within 0.000001? Find the approximate value to within 0.000001.c. Determine is this series if absolutely or conditionally convergent.
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Calculus

11/09/23

This is a series that I could use some help with solving. Could I get some help solving this series please? Thanks much!!!
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Calculus

11/09/23

This is a series that I could use some help with solving. Could I get some help solving this series please? Thanks much!!!
1a. b. How many terms are needed to approximate this series to within 0.01? Find the approximate value to within 0.01.c. Determine if this series is absolutely or conditionally convergent.
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Calculus

11/09/23

How quickly is the level of the water rising?
a trough in the shape of a triangular prism is being filled at a rate of 5 cc per minute. THe depth and width of the trough are both 50 cm, while the length is 150cm. How quickly is the level of... more
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Calculus Math

11/09/23

How would I do this?
given the function g(x) = { x+b, x < 0} {cos(x), x ≥ 0}find the value of b if any that will make the function differentiable at x = 0
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