Chapter 1.

1.1 Problem Statement

{2,4,6,8}
{2,3,4,5}
$a*$b

Evaluate the limit.

1.2 Step 1

L'Hôpital's Rule states that for functions f(x) and g(x) that are differentiable on an open interval containing x = a, and if f(a) = g(a) = 0, then

if the limit on the right exists or is infinite.

Question Sequence

Question 1.1

To determine whether l'Hôpital's Rule applies to the given problem, evaluate both the numerator and denominator at x = 0.

At x = 0, $a·e$b·x - $a = 1Wh3cvJ2xF4=.

At x = 0, sin(x) - x = 1Wh3cvJ2xF4=.

Correct.
Incorrect.

Question 1.2

Thus at x = 0, PMOdEMjAlCTr7j/lZi0uQA== an indeterminate form, and since both the numerator and denominator mGbLW+WbgnI0NoznNWVmYQ== differentiable on an open interval containing x = 0, l'Hôpital's Rule PXcxRRPwVznkzmRiLdM8PZPj3qw= apply.

Correct.
Incorrect.

1.3 Step 2

Apply l'Hôpital's Rule on the given limit.

Question 1.3

Where X = XV+Y/un20gdZycFkIAUKN7fBd5V6gRZjT8rpUjhz4oFWLrmO.

Correct.
Incorrect.

1.4 Step 3

Decide if can be evaluated immediately or if it requires repeating l'Hôpital's Rule by evaluating both the numerator and denominator at x = 0.

Question Sequence

Question 1.4

At x = 0, $ab·ex = hlF2UPykPxE=.

At x = 0, cos(x) = 0VV1JcqyBrI=.

Correct.
Incorrect.

Question 1.5

Thus, l'Hôpital's Rule wTwcJNb6hW67RxRANqPxnqfiqj8= apply.

Correct.
Incorrect.

1.5 Step 4

Question 1.6

Evaluate the limit.

= hlF2UPykPxE=

Correct.
Incorrect.