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Limit Calculations and Difference Quotients: A College Assignment on Continuity and Behavior of Functions

An assignment on limit calculations and difference quotients, analyzing continuity and function behavior.

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Limit Calculations and Difference Quotients: A College Assignment on Continuityand Behavior of Functions1.Determine the limit.If the limit does not exist, write DNElimx→-23x2-5x + 7To determine the limit of the functionf(x)=3x2−5x+7f(x) = 3x^2-5x + 7f(x)=3x2−5x+7 asx→−2x\to-2x→−2, we can simply substitute x=−2x =-2x=−2 into the function, since this is apolynomial and polynomials are continuous everywhere.2.Determine the limit.If the limit doesn'texist then write DNElimx→ 14xx2-1The limit does not exist because:

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