For each sequence, first use intuition to state what the following limits ought to be. (I...

 

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For each sequence, first use intuition to state what the following limits ought to be. (I don't need to see work for this part.) Then compose proofs of your claims using the definition of the limit. Remember, these are limits of sequences, so you can't just "find the limit" using precalculus/calculus methods. (a) lim 3 n+2 -1 (b) lim " ( 2 7 + 4) 2n 1 1 n+1 (c) lim Suppose that (an) and (bn) are sequences. Suppose that for all ne N, an 3 and that lim bn = 0. n-x (a) Using intuition (and maybe some insight from having taken Calculus II), determine what lim an bn should be.. n (b) Compose a proof of your claim from part (a) using the definition of the limit. For each sequence, first use intuition to state what the following limits ought to be. (I don't need to see work for this part.) Then compose proofs of your claims using the definition of the limit. Remember, these are limits of sequences, so you can't just "find the limit" using precalculus/calculus methods. (a) lim 3 n+2 -1 (b) lim " ( 2 7 + 4) 2n 1 1 n+1 (c) lim Suppose that (an) and (bn) are sequences. Suppose that for all ne N, an 3 and that lim bn = 0. n-x (a) Using intuition (and maybe some insight from having taken Calculus II), determine what lim an bn should be.. n (b) Compose a proof of your claim from part (a) using the definition of the limit.