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Quiz 4...

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Math 111: Quiz 4 October 5, 2012

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Each problem is worth 5 points. You do not have to simplify your answers. 1. Find the derivative of f (z) =

1 . z2 + 1

2. Use implicit differentiation to find the equation of the tangent line to the curve x2 + xy + y2 = 3 at the point (1, 1).

3. Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square increasing when the area is 16cm2 ?

4. Find the derivative of y = sin(x2 ).

Bonus: (1 pt.) Of the digits 0, 1, 2, . . . , 8, 9, which is the last to make its first appearance in the decimal representation of π ?...