Questions from General Calculus


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

Sketch the graph of a function f for which f(0) = 0, f’(0) = 3, f’(1) = 0, and f’(2) = -1.

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Q: Sketch the graph of a function g for which /

Sketch the graph of a function g for which

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Q: Sketch the graph of a function g that is continuous on its

Sketch the graph of a function g that is continuous on its domain (-5, 5) and where g(0) = 1, g’(0) = 1, g’(-2) = 0, limx→-5+ g(x) = ∞, and limx→5- g(x) = 3.

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Q: Sketch the graph of a function f where the domain is (-

Sketch the graph of a function f where the domain is (-2, 2), f’(0) = -2, lim x→-2 f(x) = ∞, f is continuous at all numbers in its domain except (1, and f is odd.

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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: a. If F(x) = 5x/(1 +

a. If F(x) = 5x/(1 + x2), find F’(2) and use it to find an equation of the tangent line to the curve y = 5x/(1 + x2) at the point (2, 2). b. Illustrate part (a) by graphing the curve and the tangent...

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Q: Determine the infinite limit. /

Determine the infinite limit.

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Q: a. If G(x) = 4x2 - x3,

a. If G(x) = 4x2 - x3, find G’(a) and use it to find equations of the tangent lines to the curve y = 4x2 - x3 at the points (2, 8) and (3, 9). b. Illustrate part (a) by graphing the curve and the ta...

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Q: Find f’(a). f(x) = 3x2

Find f’(a). f(x) = 3x2 - 4x + 1

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