Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 3

The limit is equal to 105

Work Step by Step

$\lim\limits_{x \to 3}$ $5x^{3}$ - $3x^{2}$ + x -6 We use the fact that the limit of a sum is a sum of limits and the fact that the limit of a difference is the difference of limits to expand this expression to: (1 )$\lim\limits_{x \to 3}$ $5x^{3}$ - $\lim\limits_{x_ \to 3}$ $3x^{2}$ + $\lim\limits_{x_ \to 3}$ x - $\lim\limits_{x_ \to 3}$ 6 We can now evaluate this limit term by term. Using the Direct Substitution Property we can plug in 3 for all values of x in expression (1). =$5(3)^{3} - 3(3)^{2} + 3 - 6$ =135 - 27 + 3 - 6 = 105

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