2. Find the limits. (a) limx??1?x2?2x?32x2+3x+1? (b) limt??3?2t2+7t+3t2?9? (c) limx?16?16x?x24?x?? (d) limx?0?(x2?1)(2?cosx) (c) limt?0?(t1+t?1??t1?) (f) limh?0?h(x+h)21??x21?? 3. Use the Squeeze Theorem to show that limx?0?x3+x2?sinx??=0 4. If f(x)=?2x3?x2?2x?1?, determine whether limx?0.5?f(x) exists. 5. Explain why the function is discontinuous at the given number a, and determine which kind : removable or infinite discontinuity or jump discontinuity ? (a) f(x)=x?1x4?1?,a=1 (b) f(x)={1?x2x1?? if x<1 if x?1?,a=1 6. For what values of the constants a and b are the function f continuous on (??,?)f(x)=????x?2x2?4?ax2?bx+32x?a+b? if x<2 if 2?x<3 if x?3? 7. Find numbers a and b such that limx?0?xax+b??2?=1 8. Show that there is a root of the equation cosx=x3 between 0 and 1 .