Questions from Calculus


Q: Determine the set of points at which the function is continuous.

Determine the set of points at which the function is continuous.

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Q: At the beginning of this section we considered the function and guessed

At the beginning of this section we considered the function and guessed on the basis of numerical evidence that f (x, y) → 1 as (x, y) → (0, 0). Use polar coordinat...

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Q: Find the limit, if it exists, or show that the

Find the limit, if it exists, or show that the limit does not exist.

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Q: Find the limit, if it exists, or show that the

Find the limit, if it exists, or show that the limit does not exist.

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Q: A medieval city has the shape of a square and is protected

A medieval city has the shape of a square and is protected by walls with length 500 m and height 15 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m. Your...

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Q: The gas law for a fixed mass m of an ideal gas

The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant. Show that

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Q: For the ideal gas of Exercise 88, show that

For the ideal gas of Exercise 88, show that Exercise 88: The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant....

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Q: The wind-chill index is modeled by the function

The wind-chill index is modeled by the function W = 13.12 + 0.6215T - 11.37v0.16 + 0.3965Tv 0.16 where T is the temperature (°C) and v is the wind speed (km/h). When T − 215°C and v − 30 km/h, by ho...

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Q: Find the first partial derivatives of the function. f (

Find the first partial derivatives of the function. f (x, y) = x4 + 5xy3

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Q: Find the first partial derivatives of the function. f (

Find the first partial derivatives of the function. f (x, y) = x2y - 3y4

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