Questions with detailed step by step solutions from Differential Calculus

Topics covered under Differential Calculus
Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.
Sandwich Theorem and Trigonometric Functions
Limit of Exponential and Logarithmic Function
Algebra of Continuous Functions
First Principle of Differentiation
Differentiation of Implicit Functions
Differentiation by Substitution
Differentiation of an Infinite Expression
Differentiation of Determinants
Rolle's Theorem and Intermediate Value Theorem
Lagrange's Mean Value Theorem
Taylor's and Maclaurin's Series
Approximations and Differentials
Applications on Geometrical Figures
Continuity and Differentiability
Algebra of Derivative of Functions
Differentiation of Functions in Parametric Form
Nature of Roots of Polynomial Function
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