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Unformatted text preview: Math 105 Final 1a. Determine whether the following improper integral is convergent or divergent. If it is conver- gent, compute the integral. Z 5 1 25- x 2 dx. 1b. Let F ( x ) = R cos( x ) sin( x ) e- t 2 dt . Compute F ( x ) 1c. Numerical integration Use the Midpoint Rule with n = 3 to approximate the following integral: Z 2 . 5 1 ( x- 1) 2 dx 1d. Determine whether or not the following limit exists: lim ( x,y ) (5 , 5) x 2 + y 2- 2 yx x- y 1e. Consider the quadric surface defined by the equation z = 4 x 2- 9 y 2 . Draw level curves corresponding to the values z = 0 , 1 , 2. Identify the quadric surface (i.e. is it a paraboloid, hyperboloid, or ellipsoid?) 2. Consider the following Demand and Supply curves: D ( q ) = 6- q S ( q ) = q 2 . Find the equilibrium point ( p e , q e ), and compute the Consumers and Producers surplus. 1 3. A company estimates that the income produced at time t by its factory will equal 1000- 50 t ....
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