Question

Determine the infinite limit.

lim (x + 6) / (x + 7)
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Answer 1

`\lim_(x \to \infty) (x+6)/(x+7)` = 1

Explanation:

You have to calculate the following limit:

`\lim_(x \to \infty) (x+6)/(x+7)`

To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.

`\lim_(x \to \infty) (x+6)/(x+7)= \lim_(x \to \infty)(x(1+(6)/(x)))/(x(1+(7)/(x)))=\lim_(x \to \infty)(1+6/x)/(1+7/x)=(1+0)/(1+0)=1`

Hence, the limit is 1, L = 1