let m(x)=sec x+cot^(-1)x. find m(0.3). round your answer to three decimal places. do not type any spaces in…

Explanation:

Step1: Recall secant and arccotangent definitions

We know that $\sec x=\frac{1}{\cos x}$ and we need to find $\sec(0.3)+\cot^{-1}(0.3)$. First, find $\sec(0.3)$. Since $\sec(0.3)=\frac{1}{\cos(0.3)}$, and $\cos(0.3)\approx0.955336$. So $\sec(0.3)=\frac{1}{\cos(0.3)}\approx\frac{1}{0.955336}\approx1.04676$.

Step2: Find the value of arccotangent

We know that $\cot^{-1}(x)$ has a range of $(0,\pi)$. Using a calculator, $\cot^{-1}(0.3)\approx1.287002$.

Step3: Calculate the sum

$m(0.3)=\sec(0.3)+\cot^{-1}(0.3)\approx1.04676 + 1.287002=2.333762$. Rounding to three - decimal places, we get $2.334$.

Answer:

2.334