Limits and ContinuityMTP Sep 24 Series IIQuestion 2009 of 32
All Questions

What is the value of lim⁡y→2y2−4y−2\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}

Options

A2
B4
C1
D0
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Correct Answer

✅ Option b — 4

All Options:

  • A2
  • B4
  • C1
  • D0

Detailed Solution & Explanation

To evaluate the limit lim⁡y→2y2−4y−2\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}:
First, factor the numerator using the difference of squares identity a2−b2=(a−b)(a+b)\displaystyle a^2 - b^2 = (a-b)(a+b):
y2−4=(y−2)(y+2)y^2 - 4 = (y - 2)(y + 2)
Substitute this factorization into the limit:
lim⁡y→2(y−2)(y+2)y−2\lim_{y \to 2} \frac{(y-2)(y+2)}{y-2}
For y≠2\displaystyle y \neq 2, we can cancel the common factor of (y−2)\displaystyle (y - 2) in both numerator and denominator:
lim⁡y→2(y+2)\lim_{y \to 2} (y + 2)
Substituting y=2\displaystyle y = 2 directly:
2+2=42 + 2 = 4
Thus, the limit is equal to 4\displaystyle 4.
Therefore, the correct choice is **Option B**.

More Questions from Limits and Continuity

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