Question

In Problems 7– 42, find each limit algebraically

$\underset{x\to 3}{\lim }(2-5x)$

Short answer

The value of the limit is$-13$

Step-by-step solution

Step 1. Given Information

The given limit of the function is $\underset{x\to 3}{\lim }(2-5x)$

We need to find the value of the limit.

Step 2. Expanding the limit

We know,

$\underset{x\to c}{\lim }\left[f\right(x)-g(x\left)\right]=\underset{x\to c}{\lim }f\left(x\right)-\underset{x\to c}{\lim }g\left(x\right)$

Therefore,

$\underset{x\to 3}{\lim }(2-5x)=\underset{x\to 3}{\lim }2-\underset{x\to 3}{\lim }5x$

Step 3. Value of the limit

The expression is simplifies as

$$\begin{gathered} \underset{x\to 3}{\lim }(2-5x)=\underset{x\to 3}{\lim }2-\underset{x\to 3}{\lim }5x \\ =2-5\times 3 \\ =2-15 \\ =-13 \end{gathered}$$