Question

The function,

$\ln x={\int }_1^x\frac{1}{t}dt$

is continuous and differentiable on the interval ____ .

Short answer

The function is continuous and differentiable on the interval $(0,\infty )$.

Step-by-step solution

Step 1. Given information. 

We are given a function,

$\ln x={\int }_1^x\frac{1}{t}dt$

Step 2. Completing the statement. 

We know that the given function is continuous and differentiable on the interval $(0,\infty )$.