What is the value of limy → 2 y2-4/y-2

Option b: 4. Solution: To evaluate the limit limy → 2 y2-4/y-2 : First, factor the numerator using the difference of squares identity a2 - b2 = (a-b)(a+b) : y2 - 4 = (y - 2)(y + 2) Substitute this factorization into the limit: limy → 2 (y-2)(y+2)/y-2 For y ≠ 2 , we can cancel the common factor of (y - 2) in both numerator and denominator: limy → 2 (y + 2) Substituting y = 2 directly: 2 + 2 = 4 Thus, the limit is equal to 4 . Therefore, the correct choice is Option B.

What is the value of $\lim_{y \to 2} \frac{y^2-4}{y-2}$

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

Basic Applications of CalculusMCQMTP Sep 24 Series IIQuestion 2009 of 32

All Questions

What is the value of $\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}$

Options

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Correct Answer

✅ Option b — 4

All Options:

Detailed Solution & Explanation

To evaluate the limit

\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}

:
First, factor the numerator using the difference of squares identity

\displaystyle a^2 - b^2 = (a-b)(a+b)

y^2 - 4 = (y - 2)(y + 2)

Substitute this factorization into the limit:

\lim_{y \to 2} \frac{(y-2)(y+2)}{y-2}

For

\displaystyle y \neq 2

, we can cancel the common factor of

\displaystyle (y - 2)

in both numerator and denominator:

\lim_{y \to 2} (y + 2)

Substituting

\displaystyle y = 2

directly:

2 + 2 = 4

Thus, the limit is equal to

\displaystyle 4

.
Therefore, the correct choice is **Option B**.

About This Chapter: Basic Applications of Calculus

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Limits, Continuity, Derivatives, Integrals

This chapter covers Limits, Continuity, Derivatives, Integrals and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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