Use the formal definition of the limit to prove the statement rigorously.lim(3x² + x) = 4x+1Consider the following proof.Let e > O be given. We bound | (3x² + x) - 41 using quadratic factoring.|(3x² + x)-4= |3x² +x-4| = |(3x+4)(x-1)| = |x1||3x + 41Let 6 = min(1, e). Since |x - 1|< 6 < 1, we get |3x + 4| < 7, so that|(3x² + x)-41= |x1||3x + 41 < 7|x1|Since |x1|< < e, we get|(3x²+x)-41 < 7|x1|<7.ethus proving the limit rigorously.Is this proof valid? If not, identify some reasons why.(Select all that apply.)The proof is not valid; you must assume > > e.The proof is not valid; you need to establish | (3x2 + x) - 4|

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Use the formal definition of the limit to prove the statement rigorously. lim(3x² + x) = 4 [fx Consider the following proof. Let e > 0 be given. We bound | (3x2 + x) - 41 using quadratic factoring. |(3x² + x)-4=13x² + x - 4| = |(3x+4)(x-1)| = |x1||3x + 41 Let = min(1, e). Since |x1| << 1, we get |3x + 41 < 7, so that |(3x² + x)-41= |x - 1||3x + 4| < 7|x - 1| Since |x1|< < e, we get |(3x²+x) 41 < 7|x1|<7.e thus proving the limit rigorously. Is this proof valid? If not, identify some reasons why. (Select all that apply.) The proof is not valid; you must assume >> e. The proof is not valid; you need to establish | (3x2 + x) - 41