Exercise 5.4.7. (a) First prove the following general lemma: Let f be defined on an open...

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Exercise 5.4.7. (a) First prove the following general lemma: Let f be defined on an open interval J and assume f is differentiable at a e J. If (an) and (bn) are sequences satisfying an < a < bn and lim an = lim b, = a, show f(b,) – f(an) bn - an f'(a) = lim [8 pts] Identify the curve r= 2 sine, by finding a Cartesian equation for the curve. %3D [8 pts] Find a polar equation for the curve represented by the Cartesian equation x - 2y. y -1+, at [8 pts] Find the slope of the tangent line to the curve x - Int, 1 = 1. 4) An 82-kg diver stands at the edge of a that are 1.6 m apart, as shown in the figu 5.0 m 1.6 m A B Iwo Exercise 5.4.7. (a) First prove the following general lemma: Let f be defined on an open interval J and assume f is differentiable at a e J. If (an) and (bn) are sequences satisfying an < a < bn and lim an = lim b, = a, show f(b,) – f(an) bn - an f'(a) = lim [8 pts] Identify the curve r= 2 sine, by finding a Cartesian equation for the curve. %3D [8 pts] Find a polar equation for the curve represented by the Cartesian equation x - 2y. y -1+, at [8 pts] Find the slope of the tangent line to the curve x - Int, 1 = 1. 4) An 82-kg diver stands at the edge of a that are 1.6 m apart, as shown in the figu 5.0 m 1.6 m A B Iwo

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