Questions from General Calculus


Q: Find the orthogonal trajectories of the family of curves. Use a

Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = x/1 + kx

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Q: An integral equation is an equation that contains an unknown function f

An integral equation is an equation that contains an unknown function f (x) and an integral that involves y (x). Solve the given integral equation. [Hint: Use an initial condition obtained from the in...

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Q: An integral equation is an equation that contains an unknown function f

An integral equation is an equation that contains an unknown function f (x) and an integral that involves y (x). Solve the given integral equation. [Hint: Use an initial condition obtained from the in...

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Q: An integral equation is an equation that contains an unknown function f

An integral equation is an equation that contains an unknown function f (x) and an integral that involves y (x). Solve the given integral equation. [Hint: Use an initial condition obtained from the in...

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Q: Find a function f such that f (3) = 2

Find a function f such that f (3) = 2 and (t2 + 1) f'(t) + [f (t)]2 + 1 = 0, t ≠ 1 [Hint: Use the addition formula for on Reference Page 2.]

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Q: Solve the initial-value problem in Exercise 27 in Section 7

Solve the initial-value problem in Exercise 27 in Section 7.2 to find an expression for the charge at time t. Find the limiting value of the charge.

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Q: In Exercise 28 in Section 7.2 we discussed a differential

In Exercise 28 in Section 7.2 we discussed a differential equation that models the temperature of a cup of coffee in a room. Solve the differential equation to find an expression for the temperature o...

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Q: In Exercise 15 in Section 7.1 we formulated a model

In Exercise 15 in Section 7.1 we formulated a model for learning in the form of the differential equation dP/dt = k (M – P) where P (t) measures the performance of someone learning a skill after a tra...

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Q: Find the first 40 terms of the sequence defined by and a1

Find the first 40 terms of the sequence defined by and a1 = 11. Do the same if a1 = 22. Make a conjecture about this type of sequence.

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Q: In an elementary chemical reaction, single molecules of two reactants A

In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A + B → C. The law of mass action states that the rate of reaction is...

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