Limits and Derivatives Class 11 Maths Notes – Formulas & Quick Revision

Limits and Derivatives calculus ka entry point hai — standard limits aur first-principle derivatives yahan se shuru hote hain. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Limits and Derivatives

• lim(x→0) sinx/x = 1; lim(x→0) tanx/x = 1
• lim(x→0) (eˣ−1)/x = 1; lim(x→0) (aˣ−1)/x = ln a
• lim(x→0) ln(1+x)/x = 1
• lim(x→a) (xⁿ−aⁿ)/(x−a) = n·aⁿ⁻¹
• Derivative (first principle): f′(x) = lim(h→0) [f(x+h)−f(x)]/h
• d/dx(xⁿ) = nxⁿ⁻¹; d/dx(sinx) = cosx; d/dx(cosx) = −sinx
• Product rule: (uv)′ = u′v + uv′
• Quotient rule: (u/v)′ = (u′v − uv′)/v²

Quick Revision Points

• 0/0 form mein factorize/rationalize karo ya standard limit lagao
• LHL = RHL tabhi limit exist karti hai
• Trig limits mein radians hi use hote hain
• First principle se sinx, cosx, xⁿ ke derivatives practice karo
• Ye chapter Class 12 Calculus ka gateway hai

FAQ

Standard limits kitne rato?

8-10 core limits — PDF ke one-page limit sheet mein sab grouped hain.

First principle boards mein aata hai?

Haan, 4-marker — steps ka fixed pattern PDF mein solved hai.

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