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Evaluate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
Evaluate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
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Q1
Evaluate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
3/5
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Infinity
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Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 0)/(5 - 0) = 3/5.
Questions & Step-by-step Solutions
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Q
Q: Evaluate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4)
Solution:
Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 0)/(5 - 0) = 3/5.
Steps: 9
Show Steps
Step 1: Identify the limit we want to evaluate: 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, 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 both approach 0.
Step 7: Substitute 0 for 2/x^2 and 4/x^2 in the limit: lim (x -> ∞) (3 + 0)/(5 - 0).
Step 8: This simplifies to 3/5.
Step 9: Therefore, the limit is 3/5.
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