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The spring 2010 math 220 test 2 for sections al1 and bl1. The test covers various topics related to derivatives and limits, including finding derivatives of functions such as csc x, cot x, sinโ1 x, and tanโ1 x, as well as finding derivatives using given functions and equations. The test also includes questions on finding slopes of tangent lines, increasing rates of a circular plate's area, and identifying intervals where a function's graph is decreasing.
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MATH 220 (sections AL1 and BL1) Test 2 Spring 2010
(a) d dx (csc x) =
(b) d dx
(cot x) =
(c) d dx
( sinโ^1 x
(d) d dx
( tanโ^1 x
(e) d dx (3x) =
( t^8 โ 10 t^2 + 5
)
given that y = xln^ x
The graph of f (x) is decreasing upon which one of the following intervals?
(a) (โ 2 , 2) (b) (โ 1 , 2)
(c) (0, 2) (d) (โโ, 2)
(e) (โโ, โ1) (f) (โโ, 0)
(g) (โ 2 , โ) (h) (โ 1 , โ)
(i) (0, โ) (j) (โโ, โ)
(a) lim xโ 0 cos x sin^2 x
(b) lim xโ 0 e^6 x^ โ 6 x โ 1 x^2
