117k views
4 votes
Compute lim (x → 2) (√x - √2) / (√(x+1) - √3) Refer to this as limit 1 Now say I have lim (x → a) (√x - √b) / (√(x+1) - √c)

User Lumartor
by
7.9k points

1 Answer

4 votes

Final answer:

To compute the limit (x → 2) (√x - √2) / (√(x+1) - √3), we can use the conjugate method. By multiplying the numerator and denominator by (√(x+1) + √3), we can simplify the expression. This results in (√x - √2)(√(x+1) + √3) in the numerator and (√(x+1) - √3)(√(x+1) + √3) in the denominator.

Step-by-step explanation:

To compute the limit lim (x → 2) (√x - √2) / (√(x+1) - √3), we can use the conjugate method. By multiplying the numerator and denominator by (√(x+1) + √3), we can simplify the expression. This results in (√x - √2)(√(x+1) + √3) in the numerator and (√(x+1) - √3)(√(x+1) + √3) in the denominator.

Expanding these expressions gives (√(x^2 + x + √3x + √x) - √2√(x+1) - √2√3) / (x+1 - 3). Simplifying further, (√(x^2 + x + √3x + √x) - 2√(x+1) - √6) / (x-2).

Finally, we substitute x = 2 into this expression to find the limit. Plugging in x = 2 gives (√(4 + 2 + √3(2) + 2) - 2√(2+1) - √6) / (2-2). After further simplification, we get (√(8 + √6) - 2√3 - √6) / 0. This means that the limit is undefined.

User Anthony Tietjen
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories