Please remember this is an individual test. Do not discuss the test before completing it. Do not post any questions or information about this test anywhere online. Throughout the exam, annotate and explain your calculations. Answers that are just calculations without any explanation will not receive full marks, even if they are correct. 1. Calculate these limits. (9) (xZ4) sin )4: a) link-'0 x cos x (XZ7x+10)ln x b) link>5 x210x+25 2'03 +4x+1)X5 c) limxsm X,_x5+9 2. Calculate these derivatives. (10) d xz sin(5x) 3' E x+1 d_3 3 x b) \"3x e 3. Consider this function (4) f(x) = x3 + 4 defined on the domain x e [0, 4]. The derivative of this function is a quadratic, and measure the slope, and the definite integral of the function is a quartic, and measure the area under the curve (starting, say, at x = 0 ). Explain why the derivative decreases the degree of the polynomial and the integral increases, and why the slope should be measured by a quadratic while the area is measured by a quartic. n