**Unformatted text preview: **f ( x ) = sin x centered at a = 0. (4) Use Taylor series to evaluate lim x → x 2 / 2-1 + cos x x 4 . (5) Consider the parametric curve x = t 2 + 4, y = 6-t for-∞ < t < ∞ . Eliminate the parameter to obtain an equation in x and y . Evaluate dy/dx at (5 , 5). (6) Find an equation of the line tangent to the cycloid x = t-sin t , y = 1-cos t at the point corresponding to t = π/ 6. (7) Write the equation r 2 + r (2 sin θ-6 cos θ ) = 0 in Cartesian coordinates and identify the corresponding curve. (8) Find all the points where the curve r = 4+2 sin θ has vertical and horizontal tangent lines. (9) Find the area enclosed by all the leaves of the rose r = 3 sin 4 θ . (10) Find the area inside the lima¸con r = 2 + cos θ and outside the circle r = 2. (11) Graph the conic section x 2-y 2 / 2 = 1. (12) Graph the conic section x 2 / 4 + y 2 / 25 = 1. (13) Graph the conic section r = 3 1-2 cos θ ....

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- Fall '08
- SURGENT
- Calculus, Parametric equation, Conic section