1. Use the definition of limit to show that 2n2-3n +1 lim = 2. 5n +...

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1. Use the definition of limit to show that 2n2-3n +1 lim = 2. 5n + n2) 2. Let ri= I and an+1 = In/2 +3 for n >1. Show: (i) (rn) is monotonically increasing. (ii) (In) converges to 6. 3. Show directly from the definition that the sequence 1 1 In = 1+ %3D n2 is a Cauchy sequence. 4. Show by definition that the sequence (n/3) is not a Cauchy sequence but for any positive integer k, lim |(n + k)/3 – n'/8| = 0. %3D 5. Use the definition of limit to establish the following limits. (1) lim,-2 1/(1 - r) = -1. (2) lim,-0z2/1피 =0. (3) lim,-c = c, where c is any positive number. 1 1. Use the definition of limit to show that 2n2-3n +1 lim = 2. 5n + n2) 2. Let ri= I and an+1 = In/2 +3 for n >1. Show: (i) (rn) is monotonically increasing. (ii) (In) converges to 6. 3. Show directly from the definition that the sequence 1 1 In = 1+ %3D n2 is a Cauchy sequence. 4. Show by definition that the sequence (n/3) is not a Cauchy sequence but for any positive integer k, lim |(n + k)/3 – n'/8| = 0. %3D 5. Use the definition of limit to establish the following limits. (1) lim,-2 1/(1 - r) = -1. (2) lim,-0z2/1피 =0. (3) lim,-c = c, where c is any positive number. 1

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