Question

In Problems 1– 6, find each limit

$\underset{x\to 3}{\lim }\left(-x^2+3x-5\right)$

Short answer

The value of the limit is$-5$

Step-by-step solution

Step 1. Given data

Given limit is $\underset{x\to 3}{\lim }\left(-x^2+3x-5\right)$

We have to find the value of the given limit.

Step 2. Simplifying the limit

$$\begin{gathered} \underset{x\to 3}{\lim }\left(-x^2+3x-5\right)=\underset{x\to 3}{\lim }\left(-x^2\right)+\underset{x\to 3}{\lim }\left(3x\right)+\underset{x\to 3}{\lim }\left(-5\right) \\ \Rightarrow \underset{x\to 3}{\lim }\left(-x^2+3x-5\right)=-9+9-5 \\ \Rightarrow \underset{x\to 3}{\lim }\left(-x^2+3x-5\right)=-5 \end{gathered}$$