Advanced Placement (AP) College

omain. In the practice exam question here, x = 2 is the chosen value, of course!
f(x) =
[(2x + 1)(x-2)
x=2
k
for x = 2
for x = 2
9. Let f be the function defined above. For what value of k is f continuous at x = 2?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
ANSWER

Answers

Answer 1
To determine the value of k that would make the function f continuous at x = 2, we need to evaluate the function at x = 2 and ensure that the left-hand limit and the right-hand limit are equal at that point.

Given the function:
f(x) = [(2x + 1)(x - 2)] / (x - 2)

Let's substitute x = 2 into the function:
f(2) = [(2(2) + 1)(2 - 2)] / (2 - 2)
= [(4 + 1)(0)] / 0

At this point, we have a division by zero, which indicates that the function is undefined at x = 2. In order for the function to be continuous at x = 2, we need to find a value of k that eliminates the discontinuity.

Looking at the expression, we can see that (x - 2) appears in both the numerator and denominator. To eliminate the discontinuity at x = 2, we can cancel out the (x - 2) term.

Therefore, k should be the value that makes (x - 2) cancel out. In this case, k = 5. When k = 5, the (x - 2) terms cancel out, resulting in a simplified expression of f(x) = 2x + 1.

Hence, the correct answer is (E) 5.

Related Questions

What is crystal structure

Answers

Answer:

it is an ordered arrangement of atoms or even ions

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure

GPB 1 Week 2 today 2 unscramble the letters below
1 lopo corma
2 tilismokanmer
3 issancenare
4 sadakru
5 tanconstinople​

Answers

Here are the unscrambled words:

"lopo corma" unscrambles to "colo rampo" or "color campo.""tilismokanmer" unscrambles to "mortalismoken" or "moralist token.""issancenare" unscrambles to "resistancean" or "ancestriesan.""sadakru" unscrambles to "darksau" or "asrakud.""tanconstinople" unscrambles to "constipationel" or "saintconstantlop."

Unscrambled words are words that have been rearranged or scrambled in a random order, and the task is to rearrange the letters back into their correct order to form a valid word.

It's a word puzzle or game where you are given a set of jumbled letters and you need to figure out the original word by rearranging the letters correctly. Unscrambling words can be a fun way to test your vocabulary, language skills, and problem-solving abilities.

Learn more about puzzle on:

https://brainly.com/question/30357450

#SPJ1

The federal government taxes individuals on interest earned from state bonds. The state of Washington declares that interest earned on state bonds will be free from federal tax. The case goes to the Supreme Court. Which of the following rulings is most likely in this case? The court sides with the federal government, citing federal nullification of state laws. The court sides with the state government, citing state sovereignty regarding taxation. The court sides with the federal government, citing federal supremacy over state laws. The court sides with the state government, citing the Constitution’s necessary and proper clause.

Answers

The court is most likely to side with the federal government, citing federal supremacy over state laws.
The court is most likely to side with the federal government, citing federal supremacy over state laws.
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