Questions from General Calculus


Q: If f (x) = 3x2 – x3, find f'

If f (x) = 3x2 – x3, find f' (1) and use it to find an equation of the tangent line to the curve y = 3x2 – x3 at the point (1, 2).

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Q: If g (x) = x4 - 2, find g'

If g (x) = x4 - 2, find g' (1) and use it to find an equation of the tangent line to the curve y = x4 – 2 at the point (1, -1).

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Q: Find the limit. limx→∞ x + 2/ √

Find the limit. limx→∞ x + 2/ √9x2 + 1)

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Q: Find f'(a). f (x) = 3x2

Find f'(a). f (x) = 3x2 - 4x + 1

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Q: Sketch the graph of a function for which g (0)

Sketch the graph of a function for which g (0) = g (2) = g (4) = 0, g' (1) = g' (3) = 0 g' (0) = g' (4) = 1

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Q: Find f' (a). f (t) = 2t3

Find f' (a). f (t) = 2t3 + t

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Q: Find f' (a). f (x) = x

Find f' (a). f (x) = x-2

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Q: Find f' (a). f (x) = √

Find f' (a). f (x) = √1 - 2x

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Q: Find f' (a). f (x) = 4

Find f' (a). f (x) = 4/ √1 - x

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Q: Each limit represents the derivative of some function f at some number

Each limit represents the derivative of some function f at some number a. State such an f and a in each case.

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