When working on this assignment, please follow the guidelines listed in the prev

Question

When working on this assignment, please follow the guidelines listed in the previous assignments. Find the limits of given sequences You may use any of the theorems form Section 2.2 xn = n + 5 - n yn = n2 + 5 - n2 + 1/ n + 2 - n Let (xn) be a sequence and r (0, 1). Suppose that for every n N we have |xn - xn + 1| rn. Prove that the sequence converges. (Hint: imitate the argument used in one of the class examples.) Prove, directly from the definition, that the following limits exist. lim x2 - 5x + 4 = -2 lim 3x2 + 2x + 1 = 2 lim x3 - 5 = 3 Evaluate the following limits using the limit theorems, comparison theorem, and squeeze theorem of Section 1.1(but do not use Hospital's rule).You may assume

Explanation / Answer

lim x->a f(x) =L we will solve it step by step as given below a)lim x->3 x^2 -5x + 4 = 3^2 -5*3 +4 = 9-15+4 = -2.................................Ans b) in this case we have lim x->-1 3x^2 +2x+1 = 3*1 -2+1 =2.................................Ans c)Here we have lim x->2 x^3 -5 = 8-5 = 3................................Ans

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