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Mathematics · JEE | LIMITS AND DERIVATIVES
हिन्दीMatch List-I with List-II: List-I List-II A \( \lim_{x \to 0} x^2 \) I \( 1 \) B \( \lim_{x \to 1} x^3 \) II \( 0 \) C \( \lim_{x \to a} 3 \) (constant) III \( 3 \) D \( \lim_{x \to 0^+} \frac{1}{x^2} \) IV \( +\infty \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | \( \lim_{x \to 0} x^2 \) | I | \( 1 \) |
| B | \( \lim_{x \to 1} x^3 \) | II | \( 0 \) |
| C | \( \lim_{x \to a} 3 \) (constant) | III | \( 3 \) |
| D | \( \lim_{x \to 0^+} \frac{1}{x^2} \) | IV | \( +\infty \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option C
A-(II), B-(I), C-(III), D-(IV)
Explanation
Direct limit evaluation gives: \( \lim_{x \to 0} x^2 = 0 \), \( \lim_{x \to 1} x^3 = 1 \), limit of a constant function is the constant itself (\( 3 \)), and \( \lim_{x \to 0^+} \frac{1}{x^2} = +\infty \). Thus, A-(II), B-(I), C-(III), D-(IV).
