Questions from General Calculus


Q: If f (x) and g (x) are differentiable

If f (x) and g (x) are differentiable functions such that f (2) = f ‘(2) = 3, g (2) = 3, and g’(2) = 1/3, compute the derivative: d/dx [(g (x))2] |x=2

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Q: Simplify the following expressions. ½ ln 9

Simplify the following expressions. ½ ln 9

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Q: Simplify the following expressions. 3 ln ½ + ln 16

Simplify the following expressions. 3 ln ½ + ln 16

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Q: Simplify the following expressions. ln 4 + ln 6 -

Simplify the following expressions. ln 4 + ln 6 - ln 12

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Q: State the formula for d/dx yr, where y is

State the formula for d/dx yr, where y is defined implicitly as a function of x.

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Q: Differentiate the function using one or more of the differentiation rules discussed

Differentiate the function using one or more of the differentiation rules discussed thus far. y = 2(x3 - 1)(3x2 + 1)4

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Q: Outline the procedure for solving a related-rates problem.

Outline the procedure for solving a related-rates problem.

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Q: What is the x-intercept of the graph of the natural

What is the x-intercept of the graph of the natural logarithm function?

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Q: State the main features of the graph of y = ln x

State the main features of the graph of y = ln x.

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Q: State the two key equations giving the relationships between ex and ln

State the two key equations giving the relationships between ex and ln x.

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