CLASS 11th COMMERCE (APPLIED MATHS ) L-5 LIMIT & CONTINUITY FULL CHAPTER EXPLANATION By RAHUL SIR скачать в хорошем качестве

CLASS 11th COMMERCE (APPLIED MATHS ) L-5 LIMIT & CONTINUITY FULL CHAPTER EXPLANATION By RAHUL SIR

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
eq 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 Please 🙏 subscribe