CLASS 11th COMMERCE (APPLIED MATHS ) L-5 LIMIT & CONTINUITY FULL CHAPTER EXPLANATION By RAHUL SIR
Автор: Ud Pathshala
Загружено: 2026-02-12
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Описание:
CLASS 11th COMMERCE (APPLIED MATHS ) L-5 LIMIT & CONTINUITY FULL CHAPTER EXPLANATION By RAHUL SIR
Limits ke Basic Theorems
Agar \lim_{x \to a} f(x) = L aur \lim_{x \to a} g(x) = M ho, toh:
• Sum/Difference Rule: \lim_{x \to a} [f(x) \pm g(x)] = L \pm M
• Product Rule: \lim_{x \to a} [f(x) \cdot g(x)] = L \cdot M
• Quotient Rule: \lim_{x \to a} \frac{f(x)}{g(x)} = \frac{L}{M} (shart ye hai ki M \neq 0)
2. Standard Limits Formulas (Most Important)
Ye formulas directly questions mein apply hote hain:
Algebraic & Exponential
• Power Formula: \lim_{x \to a} \frac{x^n - a^n}{x - a} = n a^{n-1}
• Exponential: \lim_{x \to 0} \frac{e^x - 1}{x} = 1
• Logarithmic: \lim_{x \to 0} \frac{\ln(1+x)}{x} = 1
Trigonometric Limits
• Sine Rule: \lim_{x \to 0} \frac{\sin x}{x} = 1
• Tan Rule: \lim_{x \to 0} \frac{\tan x}{x} = 1
• Cos Rule: \lim_{x \to 0} \cos x = 1
3. L'Hôpital's Rule (Shortcut)
Jab limit solve karte waqt \frac{0}{0} ya \frac{\infty}{\infty} ka form bane, toh numerator aur denominator ko alag-alag differentiate kar
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