Differential and Integral Calculus by Feliciano and Uy, Exercise 1.2, Problem 6

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PROBLEM:

Evaluate lim⁡x→2(4x−3)(x2+5)\displaystyle \lim_{x\to 2}\left(4x-3\right)\left(x^2+5\right).

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SOLUTION:

Plug the value x=2.

lim⁡x→2(4x−3)(x2+5)=[(4⋅2)−3][(2)2+5]=[8−3][4+5]=(5)(9)=45  (Answer)\begin{align*} \lim\limits_{x\to 2}\left(4x-3\right)\left(x^2+5\right) & =\left[\left(4\cdot 2\right)-3\right]\left[\left(2\right)^2+5\right]\\ & =\left[8-3\right]\left[4+5\right]\\ & =\left(5\right)\left(9\right)\\ & =45 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\ \end{align*}
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