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Find the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
Find the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
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Practice Questions
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Q1
Find the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
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3/5
1
Infinity
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Dividing numerator and denominator by x^2, we get lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2) = 3/5.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
Solution:
Dividing numerator and denominator by x^2, we get lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2) = 3/5.
Steps: 8
Show Steps
Step 1: Identify the limit we want to find: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4).
Step 2: Notice that both the numerator (3x^2 + 2) and the denominator (5x^2 - 4) have the highest power of x as x^2.
Step 3: To simplify, divide every term in the numerator and the denominator by x^2.
Step 4: After dividing, the numerator becomes (3 + 2/x^2) and the denominator becomes (5 - 4/x^2).
Step 5: Now we rewrite the limit: lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2).
Step 6: As x approaches infinity, the terms 2/x^2 and 4/x^2 approach 0.
Step 7: Therefore, the limit simplifies to (3 + 0)/(5 - 0) = 3/5.
Step 8: Conclude that the limit is 3/5.
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