Use the definition of continuity and the properties of limits to show that the function is...

 

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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 35v2 + 11, == lim p(v) lim 35v + 11 v 1 = V-1 = 3 lim 5v2 + 11 = 3 V-1 lim v5v2+11) lim (5v2 = 3. V-1 = 3 = a = 1 by the Constant Multiple Law by the Root Law + lim 11 by the Sum Law (5v). VI (12) V 1 5 lim (v2+ lim 11 . v 35 (1) +11 V-1 by the Constant Multiple Law by the Direct Substitution Property Find p(1). p(1) = Thus, by the definition of continuity, p is continuous at a = 1. Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 35v2 + 11, == lim p(v) lim 35v + 11 v 1 = V-1 = 3 lim 5v2 + 11 = 3 V-1 lim v5v2+11) lim (5v2 = 3. V-1 = 3 = a = 1 by the Constant Multiple Law by the Root Law + lim 11 by the Sum Law (5v). VI (12) V 1 5 lim (v2+ lim 11 . v 35 (1) +11 V-1 by the Constant Multiple Law by the Direct Substitution Property Find p(1). p(1) = Thus, by the definition of continuity, p is continuous at a = 1.