Finding the Limit of a Product

Find:

1. \(\lim\limits_{x\rightarrow 3}x^{2}\)
2. \(\lim\limits_{x\rightarrow -5}(-4x)\)

Solution

1. \(F( x) =x^{2}\) is the product of two functions, \(f(x)=x\) and \(g(x)=x\). Then, using the Limit of a Product, we have \[ \lim_{x\rightarrow 3}x^{2}=\lim_{x\rightarrow 3}x\cdot \lim_{x\rightarrow 3}x=(3)(3)=9\]
2. \(F(x)=-4x\) is the product of two functions, \(f(x)=-4\) and \( g(x)=x\). Then, using the Limit of a Product, we have \[ \lim\limits_{x\rightarrow -5}(-4x)=\lim_{x\rightarrow -5}(-4)\cdot \lim\limits_{x\rightarrow -5}x=(-4)(-5)=20\]