Lim x-->infinity 10/x+10 find the limit

To find the limit of the given expression as x approaches infinity, we need to simplify the expression and observe its behavior as x gets larger and larger.

The given expression is:
lim x→∞ (10/x + 10)

To simplify this expression, we can divide both terms of the numerator and denominator by x:
lim x→∞ (10/x + 10) = lim x→∞ (10/x * 1/x + 10)

Next, we can break down the expression into separate limits:
= lim x→∞ (10/x) * lim x→∞ (1/x) + lim x→∞ (10)

Now, let's analyze each term separately:
1. lim x→∞ (10/x):
As x approaches infinity, the term 10/x approaches zero because the denominator (x) is increasing without bound. Therefore, lim x→∞ (10/x) = 0.

2. lim x→∞ (1/x):
Similarly, as x gets larger and larger, the term 1/x also approaches zero because dividing any constant by an infinitely large number results in a very small value. Hence, lim x→∞ (1/x) = 0.

3. lim x→∞ (10):
This term does not depend on x, so it remains constant as x approaches infinity. Therefore, lim x→∞ (10) = 10.

Now we can substitute these values back into our original expression:
lim x→∞ (10/x + 10) = 0 * 0 + 10 = 10

Therefore, the limit of the expression as x approaches infinity is 10.