Class XI Mathematics
Chapter 12: Limits and Derivatives
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Syllabus Sections
Key Formulas & Equations
Click Copy to duplicateStandard Trig Limit
\lim_{x \to 0} \frac{\sin x}{x} = 1
Fundamental trigonometric limit.
Quotient Rule of differentiation
\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}
Differentiates division of two functions.
Related Formulas from Adjacent Chapters
3D Distance Formula
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}
[From Introduction to Three Dimensional Geometry] Euclidean distance between two coordinates in 3D space.
Grouped Variance
\sigma^2 = \frac{\sum f_i(x_i - \bar{x})^2}{N}
[From Statistics] Variance of grouped frequency distribution.
Standard Deviation
\sigma = \sqrt{\sigma^2}
[From Statistics] Square root of variance, measuring dispersion in original units.