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Unformatted text preview: Practice Test 2C for Math 1501 (I) Let f be the function deﬁned by x+1 f ( x) = √ 5 + x2 for all x . (a) Find the equation for the tangent line to the graph of y = f (x) at the point (2, 1). (b) Are there any other points on the graph at which the tangent line is parallel to this one? (II) Find the slope of the parabola x = y 2 at each of the points where it intersects the circle (x − 2)2 + y 2 = 4 . (III) Let f be a funtion with f (3) = 1 and f (3) = 0. Evaluate lim f (3x) x−1 x→1 (IV) At what rate is the surface are of a sphere changing at an instant at which the radius is increasing at a rate of 1 cm/sec, and the volume is increasing at a rate of 20 cm3 /sec? (V) (a) Given a function strictly increasing function f with f (2) = 4 and f (2) = 3, compute the g (4) where g is the inverse function of f . (b) Compute the derivative of 22 ,
x (c) Compute the derivative of tan(arcsin(x)) , for (d) Compute the derivative of 1 . 1 + (x ln(x)) −1 <x< 1 ...
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