1. Calculate the following limits. (12) x' + x'(x' + x3) a lim 1 100 x3 + x2(x5+ x2) x' Inc +el(x2 + 3x) +e"(x + x3) b. lim I +:00 4x2 + 56x7 + er(x3 + x2) Va13 + all C. lim 1 +00 $ 715 + 76 1 d. lim r *00 sinc + cos 2. What is the long term behaviour of the following models? Justify your answers. (9) a. A population model (poluation in millions, time in years). 10e3t p(t) = 7+ 2e3t b. A model of concentration of H+ ions (time in seconds). t2 + 1 c(t) = 13 + + + 2 c. A model of inflation (time in year). I(t) = 3 sin(6nt) 12 7 3. If f is a bounded function defined on all of R, must it have a horizontal asymptote? Use examples or counter-examples in your argument. (4) 4. Assume f and g are functions on (0, oo). If they have the same asymptotic order and g has a horizontal asymptote, must f also have one? Reference the definition and feel free to use examples or counter-examples in your argument. (4) 5. Calculate the following derivative by definition. (6) d c' + 3x6. Calculate the following derivatives. Label the rules you used. (12) d a. sin c tan c dr d b. d x2 - 3 C. dx x2 + 7x - 9