Determine the limit as x approaches infinity for the given expression:
Question 12
\[
\lim _{x \rightarrow \infty} 7 x e^{1 / x}-7 x=
\]
Answer
So, the limit of the given expression as x approaches infinity is \(\boxed{0}\).
Step 1 ：We are given the expression \(7x e^{1 / x} - 7x\) and we are asked to find the limit as x approaches infinity.
Step 2 ：We can separate the expression into two parts: \(7x * e^{1/x}\) and \(-7x\). We can then apply the limit to each part separately.
Step 3 ：As x approaches infinity, the exponential part of the expression, \(e^{1/x}\), approaches 1. This is because the limit of \(e^{1/x}\) as x approaches infinity is 1.
Step 4 ：Therefore, the expression simplifies to \(7x - 7x\), which equals 0.
Step 5 ：So, the limit of the given expression as x approaches infinity is \(\boxed{0}\).
