MATH 1000 Midterm: MATH 1000 Midterm 2
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31 Jan 2019
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Review questions for midterm 2: compute the derivatives of: f (x) = ln(cid:16) x. 2(cid:17) ; f (x) = xln x; f (x) = x tan 1 (2x) [remark: tan 1 arctan : consider a curve given implicitly by (cid:0)x2 + y2(cid:1)2 point (1, 1). (b) estimate the value of y when x = 1. 1. = 4x2y. (a) find the slope of the tangent line at the: grain pouring from a chute at the rate of 1/4 m3/min forms a conical pile whose height is always twice its radius. How fast is the height increasing when the pile is 2m high? (remark: v = 1. 3 r2h: sketch the graphs of f (x) = x + 2x2 ; f (x) = x2ex and f (x) = x (1 + x)2. How many zeros, max/min and in ection points can it have: de ne arcsec x ; sketch its graph.
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