Asksia AI LOGO

Sia

Question
Math
Posted 3 months ago
2. limx9x4+1x23x+5\lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{4}+1}}{x^{2}-3 x+5} is
(A) 1
(B) 3
(C) 9
(D) nonexistent
Sign in to unlock the answer
Answer from Sia
Posted 3 months ago
Solution by Steps
step 2
Simplifying the expression, we get limx9+1x413x+5x2 \lim_{x \to \infty} \frac{\sqrt{9 + \frac{1}{x^4}}}{1 - \frac{3}{x} + \frac{5}{x^2}} ..
step 3
As x x approaches infinity, the terms 1x4 \frac{1}{x^4} , 3x \frac{3}{x} , and 5x2 \frac{5}{x^2} approach zero..
step 4
The limit then simplifies to limx91 \lim_{x \to \infty} \frac{\sqrt{9}}{1} ..
step 5
The final result is 3 3 ..
B
Key Concept
Limit of a Rational Function with a Radical as x x Approaches Infinity
Explanation
When finding the limit of a rational function with a radical as x x approaches infinity, divide by the highest power of x x in the denominator and simplify. Terms with x x in the denominator approach zero, and the limit can be evaluated by substituting the remaining terms.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question