Questions from General Calculus


Q: If f (x) = 2x + ln x, find

If f (x) = 2x + ln x, find f-1 (2).

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Q: Find the inverse function of f (x) = x +

Find the inverse function of f (x) = x + 1/2x + 1.

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Q: Find the exact value of each expression. (a).

Find the exact value of each expression. (a). e2ln3 (b). log 1025 + log104

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Q: Make a rough sketch of the graph of the function. Do

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3. Figures 3: Figures 13...

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Q: Solve each equation for x. (a). ex =

Solve each equation for x. (a). ex = 5 (b). ln x = 2 (c). eex = 2

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Q: The half-life of palladium-100, 100Pd, is

The half-life of palladium-100, 100Pd, is four days. (So, half of any given quantity of 100Pd will disintegrate in four days.) The initial mass of a sample is one gram. (a). Find the mass that remains...

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Q: The population of a certain species in a limited environment with initial

The population of a certain species in a limited environment with initial population 100 and carrying capacity 1000 is where is measured in years. P (t) = 100,000/100 + 900e-t (a). Graph this function...

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Q: If f (x) = x2 -2x + 3,

If f (x) = x2 -2x + 3, evaluate the difference quotient f (a + h) – f (a)/ h.

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Q: Graph the three functions y = xa, y = ax,

Graph the three functions y = xa, y = ax, and y = logax on the same screen for two or three values of a > 1. For large values of x, which of these functions has the largest values and which has the sm...

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Q: (a). Sketch the curve represented by the parametric equations x

(a). Sketch the curve represented by the parametric equations x = et, y = √t, 0 < t < 1, and indicate with an arrow the direction in which the curve is traced as increases. (b). Eliminate the paramete...

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