Chapter 14: Q. 5 (page 907)

In Problems 1– 6, find each limit
$\lim_{x \to 5} [(3 x) (x - 2)^{2}]$

Short Answer

Expert verified

The value is $135$

Step by step solution

Step 1. Rewriting the limit

The function can be rewritten as,

$(3 x) (x - 2)^{2} = 3 x (x^{2} - 4 x + 4) = 3 x^{3} - 12 x^{2} + 12 x$

Therefore,

$\lim_{x \to 5} [(3 x) (x - 2)^{2}] = \lim_{x \to 5} (3 x^{3} - 12 x^{2} + 12 x)$

Step 2. Simplifying the limit

$\lim_{x \to 5} [(3 x) (x - 2)^{2}] = \lim_{x \to 5} (3 x^{3} - 12 x^{2} + 12 x) \lim_{x \to 5} (3 x^{3} - 12 x^{2} + 12 x) = \lim_{x \to 5} 3 x^{3} - \lim_{x \to 5} 12 x^{2} + \lim_{x \to 5} 12 x = 3 (5)^{3} - 12 (5)^{2} + 12 (5) = 375 - 300 + 60 = 135$

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In Problems 1– 6, find each limit
$\lim_{x \to 5} [(3 x) (x - 2)^{2}]$

Short Answer

Step by step solution

Step 1. Rewriting the limit

Step 2. Simplifying the limit

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In Problems 1– 6, find each limitlimx→5(3x)(x-2)2

Short Answer

Step by step solution

Step 1. Rewriting the limit

Step 2. Simplifying the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In Problems 1– 6, find each limit
$\lim_{x \to 5} [(3 x) (x - 2)^{2}]$