Problem 10: Consider the polar curve given by the equation r(0) = 4 + 4 cos(0). It is an example of what is sometimes called a cardiod. a) Sketch a graph of the cardiod. (2 pts) b) Find an equation of the line tangent to the cardiod at the point (4, 2 ). Give an expression for the exact value and then, if it is not an integer, round it to three decimal places. (4 pts) c) Find the area of the region bounded by the curve. (4pts) Problem 11: Consider the following convergent series. K=0 * 2 + 1 a) Use Theorem 10.13 that I've included below to find an upper bound for the remainder, Rn, in terms of n. (2 pts) b) Then find how many terms are needed to ensure that the remainder is less than 10-3. (2 pts) THEOREM 10.13 Estimating Series with Positive Terms Let f be a continuous, positive, decreasing function for x 2 1 and let a, = f(k) for k = 1, 2, 3, .... Let S= >, a, be a convergent series and let Sn = __ a be the sum of the first n terms of the series. The remainder Rn = S - S,, satisfies Rn jax