Unformatted text preview: Practice Test 2A for Math 1501 (I) Let f be the function deﬁned by f (x) = x2 + 4 2x for x = 0 (a) Find the equation for the tangent line to the graph of y = f (x) at the point (4, 5/2). (b) Find the intersection of this tangent line with the x axis. (II) The curve given by x2 + 2y 2 + 2xy = A is an ellipse. (a) Find the smallest value of A so that this ellipse intersects the unit circle x2 + y 2 = 1 , and ﬁnd the points of intersection for this value of A. (b) Find the slope of of the unit circle at these points of intersection. (c) Find the slope of of the ellipse at these points of intersection. (III) Let x≥1 x2 , Ax + B, x < 1 . (a) For what values of A and B is f diﬀerentiable for all x? f (x) = (b) With these values of A and B , what is the equation of the tangent line to f at x = 1? (IV) A particle is moving along the parabola 4y = (x + 2)2 in such a way that its x coordinate is increasing at a constant rate of 2 units per second. How fast is the particle’s distance to the point (−2, 0) changing at the instant it is at the point (2, 4)? (V) (a) Given a function f with f (0) = 1 and f (4) = 2. Compute d f ((x − 4)2 )f (x) dx at x = 4. (b) Compute the derivative of (c) Compute the derivative of x+ (d) Compute the derivative of
2 x2 tan(x2 ) , √ x, ex . ...
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This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Tech.
 Fall '08
 N/A
 Math, Calculus

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