Limits of polynomials Use the fact that limx → c(k) = k for any number k together wi...

Limits of polynomials Use the fact that lim_{x → c}(k) = k for any number k together with the results of Exercises 1 and 3 to show that lim_{x → c} ƒ(x) = ƒ(c) for any polynomial function

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Suppose that functions ƒ₁(x), ƒ₂(x), ƒ₃(x) and have limits L₁, L₂, and L₃ respectively, as x → c. Show that their sum has limit L₁ + L₂ + L₃. Use mathematical induction (Appendix 2) to generalize this result to the sum of any finite number of functions.

Use the fact that lim_{x → c} x = c and the result of Exercise 2 to show that lim_{x → c} xⁿ = cⁿ for any integer n > 1.