Problem
1. Find values of the constants $k$ and $m$, if possible, that will make the function $f(x)$ continuous everywhere.
\[
f(x)=\left\{\begin{array}{ll}
x^{2}+5, & x>2 \\
m(x+1)+k, & -1
Solution
Step 1 ：Find the limit of the function as x approaches -1 from the left and from the right, and equate them: \(2(-1)^3 + (-1) + 7 = m(-1+1) + k\)
Step 2 ：Find the limit of the function as x approaches 2 from the left and from the right, and equate them: \(m(2+1) + k = 2^2 + 5\)
Step 3 ：Solve the system of equations to find the values of k and m: \(k = 4\) and \(m = \frac{5}{3}\)
Step 4 ：\(\boxed{k = 4, m = \frac{5}{3}}\)
From Solvely APP
Solution
Step 1 ：Find the limit of the function as x approaches -1 from the left and from the right, and equate them: \(2(-1)^3 + (-1) + 7 = m(-1+1) + k\)
Step 2 ：Find the limit of the function as x approaches 2 from the left and from the right, and equate them: \(m(2+1) + k = 2^2 + 5\)
Step 3 ：Solve the system of equations to find the values of k and m: \(k = 4\) and \(m = \frac{5}{3}\)
Step 4 ：\(\boxed{k = 4, m = \frac{5}{3}}\)
