1950 AMC 12 Problem 40

Attempt Problem 40 of the 1950 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1950 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

40.

The limit of

\dfrac{x^2-1}{x-1}

as

x

approaches

1

as a limit is:

0

Indeterminate

x-1

2

1

Answer: D

Concepts:calculus difference of squares

Difficulty rating: 1470

Small hint:

Factor the numerator as a difference of squares

Big hint:

For

x\ne1,

cancel the common factor

x-1

Solution:

For

x\ne1,

\begin{aligned} \frac{x^2-1}{x-1} &=\frac{(x-1)(x+1)}{x-1}\\ &=x+1. \end{aligned}

Therefore the limit as

x

approaches

1

is

1+1=2.

Thus, the correct answer is D.

Problem 40 in other years