8. Find the equations of both the tangent lines to the hyperbola x2 - 4yz = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola. 9. a. Find lim sinx cscox b. If g(0) = Osine, find g"("). Give exact values.4. a. Suppose that f(x) = g(x3) + e#(3x) where g' and g" exist. Find f' and f" in terms of g' and g". b. Find f", when f (x) = e* + 5* 5. Differentiate using implicit differentiation: a. V2x2 - 3y = x3y2 + 4. Do not square both sides. b. x2 cos(3y) - yz sin(x2) = 5 6. Differentiate using the logarithmic differentiation: (2x2-3)3 a. y = - (4x2-3x+1)7(6x+2)2 by = (In x)i 7. Suppose that the cost, C in dollars, of producing x units of a certain item is C(x) = 920 + 3x - 0.03x2 + 0.0006x3. a. Find the marginal cost function b. Find C'(100) and explain its meaning c. Compare C'(100) with the cost of producing the 101st item