Consider the function f(x) = 1 2x+5, which we know goes to 0 as x *....

 

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Consider the function f(x) = 1 2x+5, which we know goes to 0 as x *. a) Find some N so that 1 2x+5 <0.1 whenever x > N. b) Find some N so that 1 2x+5 <0.01 whenever x > N. c) Find some NV so that 1 2x+5 <0.001 whenever x > N. d) When we talk about limits to 0, we often use the phrase "gets closer and closer to 0", which is fudgey at best. To make this notion precise, we say that for any > > O we can find some N so that - N (the idea being that we can make & as small as we like and the function will eventually be bounded by it); note that the smaller & is, the bigger N must be. Find some NV (dependent on 6) so that 1 2x+5 < 6 whenever x > N. Consider the function f(x) = 1 2x+5, which we know goes to 0 as x *. a) Find some N so that 1 2x+5 <0.1 whenever x > N. b) Find some N so that 1 2x+5 <0.01 whenever x > N. c) Find some NV so that 1 2x+5 <0.001 whenever x > N. d) When we talk about limits to 0, we often use the phrase "gets closer and closer to 0", which is fudgey at best. To make this notion precise, we say that for any > > O we can find some N so that - N (the idea being that we can make & as small as we like and the function will eventually be bounded by it); note that the smaller & is, the bigger N must be. Find some NV (dependent on 6) so that 1 2x+5 < 6 whenever x > N.