Class 12

15. Limits, Continuity & Differentiability question bank (Maths)

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Q1.

If \( L = \lim_{x \to 0} \frac{1}{x^3} \left(\frac{1}{\sqrt{1 + x}} - \frac{1 + a x}{1 + b x}\right) \) exists, then

(A)
\( a = \frac{1}{4} \)
(B)
\( b = \frac{3}{4} \)
(C)
\( L = -\frac{1}{32} \)
(D)
\( L = \frac{1}{32} \)
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Q2.

\(f(x) = \frac{|x^3 - 3x^2 + 2x|}{x^3 - 3x^2 + 2x}\). Find the set of points \(a\) where \(\lim_{x \to a} f(x)\) does not exist.

(A)
0
(B)
1
(C)
2
(D)
3
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