Give a correct proof of the given claim

Reference no: EM131006196

1. Use the precise definition of the limit to show that lim_x→2 x/(x - 1) = 2.

2. We claim that the equation tan x/x = 3/2 has at least one positive root.

a. Consider the following proof of this claim: Let f(x) = 2 tan x - 3x. Then f(π/3) = 2√3 - π > 0 and f(π) = -3 π < 0. therefore there is c in [π/3, π] such that f(c)="0" by the intermediate value theorem. It fallows that c is a positive root of the given equation.

Explain in one sentence what ls wrong with this proof.

b. Give a correct proof of this claim.

Reference no: EM131006196

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