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JEE Main Mathematics

Limits, Continuity and Differentiability

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A timed sectional mock on this unit

Real functions and their graphs, limits, continuity and differentiability, the rules of differentiation, and rates of change, monotonic functions, maxima and minima.

Key formula
lim⁡x→0sin⁡xx=1,lim⁡x→0ex−1x=1,ddx(uv)=u′v+uv′\lim_{x \to 0} \frac{\sin x}{x} = 1, \quad \lim_{x \to 0} \frac{e^x - 1}{x} = 1, \quad \frac{d}{dx}(uv) = u'v + uv'

What this unit covers

  • Real-valued functions, algebra of functions

  • Polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions

  • Graphs of simple functions

  • Limits

  • Differentiation of the sum, difference, product and quotient of two functions

  • Continuity and differentiability

  • Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions

  • Derivatives of order up to two

  • Rate of change of quantities

  • Monotonic (increasing and decreasing) functions

  • Maxima and minima of functions of one variable

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