1. Calculate these limits. (9) (x2 4) Sin x a) llmx>0 x cos x (x27x+10) In x b) link*5 x210x+25 6" (3r2 +4x+1)x5 c) 11m,H00 x7_x5+9 2. Calculate these derivatives. (10) d x2sin(5x) a) dx x+1 b)d?x3xe 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