Limits Approximation Trick in 59 Seconds! 🔥
❓ Concept 🎬 Limits Approximation Trick Limits me jab x → 0 x \to 0 aur expression weird, lengthy, ya scary lage — toh ek hi cheez kaam aati hai 👇 👉 STANDARD APPROXIMATIONS . ✍️ Short Explanation JEE limits ka core idea yeh hai: Jab input bahut chhota ho jaata hai, functions apna linear behaviour dikhate hain. Isliye hume: exact values nahi sirf first term (leading term) chahiye hota hai 🔹 Step 1 — Angle Approximations (as x → 0) Sabse important JEE tools: sin θ ≈ θ \sin \theta \approx \theta tan θ ≈ θ \tan \theta \approx \theta tan − 1 ( x ) ≈ x \tan^{-1}(x) \approx x 📌 Reason: Small angle ⇒ curve almost straight line ban jaati hai. 👉 Agar argument small hai, bina soche replace kar do. 🔹 Step 2 — Exponential Approximation For small x x : e k x − 1 ≈ k x e^{kx} - 1 \approx kx General rule: e ( something small ) − 1 ⇒ that small thing e^{(\text{something small})} - 1 \Rightarrow \text{that small thing} 📌 Higher powers...