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2. Find the limits. (a) $lim_{x??1}x_{2}?2x?32x_{2}+3x+1?$ (b) $lim_{t??3}2t_{2}+7t+3t_{2}?9?$ (c) $lim_{x?16}16x?x_{2}4?x??$ (d) $lim_{x?0}(x_{2}?1)(2?cosx)$ (c) $lim_{t?0}(t1+t?1??t1?)$ (f) $lim_{h?0}h(x+h)1??x1??$ 3. Use the Squeeze Theorem to show that $lim_{x?0}x_{3}+x_{2}?sinx??=0$ 4. If $f(x)=?2x_{3}?x_{2}?2x?1?$, determine whether $lim_{x?0.5}f(x)$ 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) $f(x)=x?1x_{4}?1?,a=1$ (b) $f(x)={1?x_{2}x1??ifx<1ifx?1?,a=1$ 6. For what values of the constants $a$ and $b$ are the function $f$ continuous on $(??,?)$ $f(x)=????x?2x_{2}?4?ax_{2}?bx+32x?a+b?ifx<2if2?x<3ifx?3?$ 7. Find numbers $a$ and $b$ such that $lim_{x?0}xax+b??2?=1$ 8. Show that there is a root of the equation $cosx=x_{3}$ between 0 and 1 .

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