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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Limits and continuity

Grade: 1400-a Lesson: S2-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the limit of the function \$f(x) = (3x^2 - 2x + 1)/(x - 1)\$ as x approaches 1.
2	Step	To find the limit, substitute the value of x into the function and simplify	\$\lim_{x \to 1} (3x^2 - 2x + 1)/(x - 1) \$
3	Clue	Factoring the numerator	\$\lim_{x \to 1} (\cancel((x - 1))(3x + 1))/\cancel((x - 1)) \$
4	Step	After cancellation	\$\lim_{x \to 1} (3x + 1) \$
5	Step	Substituting x = 1	3(1) + 1 4
6	Step	Therefore, the limit of the function as x approaches 1 is 4.
7	Choice.A	This option corresponds to the correct answer we derived through the evaluation. It states that the limit of the function as x approaches 1 is 4, which is the result we obtained	4
8	Choice.B	This option is incorrect. The limit of the function as x approaches 1 is not 6; the correct result is 4	6
9	Choice.C	This is not correct. Similar to option B, it seems to be a result of a miscalculation. The function simplifies to 3x+1, so the limit is 4, not 10	10
10	Choice.D	This option is incorrect. We have found that the limit of the function f(x) as x approaches 1 is 4, not 14	14
11	Answer	Option	A
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the limit of the function \$f(x) = (3x^2 - 2x + 1)/(x - 1)\$ as x approaches 1.

Step

To find the limit, substitute the value of x into the function and simplify

\$\lim_{x \to 1} (3x^2 - 2x + 1)/(x - 1) \$

Clue

Factoring the numerator

\$\lim_{x \to 1} (\cancel((x - 1))(3x + 1))/\cancel((x - 1)) \$

Step

After cancellation

\$\lim_{x \to 1} (3x + 1) \$

Step

Substituting x = 1

3(1) + 1

Step

Therefore, the limit of the function as x approaches 1 is 4.

Choice.A

This option corresponds to the correct answer we derived through the evaluation. It states that the limit of the function as x approaches 1 is 4, which is the result we obtained

Choice.B

This option is incorrect. The limit of the function as x approaches 1 is not 6; the correct result is 4

Choice.C

This is not correct. Similar to option B, it seems to be a result of a miscalculation. The function simplifies to 3x+1, so the limit is 4, not 10

Choice.D

This option is incorrect. We have found that the limit of the function f(x) as x approaches 1 is 4, not 14

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?