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Questions for Differential Calculus for JEE

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Important Topics in Differential Calculus for IIT JEE

Fundamentals and Functions (Topic Weightage : 5 %)

  • Fundamentals, CLOSED AND OPEN INTERVALS, Quadratic Equations, Graphical representation of function, Fractional part function, Signum Function, Reciprocal function, Logarithmic function, Exponential function, Square root function, Polynomial function, Rational function,
  • Monotonic Function, odd and even function, Periodic function, Mapping of Function,

Limit (Topic Weightage : 5 %)

  • limits of function, Standard limits, Indeterminate forms, Sandwich theorem, Factorization method, Rationalization Method, Algebraic function of ∞ type ∞/∞ form, exponential limits, L’ Hospital’s Theorem

Continuity and Differentiability(Topic Weightage : 3 %)

  • Continuity of a function, Differentiability.

Differentiation (Topic Weightage : 1 %)

  • Derivative of standards functions, Product Rule, Quotient rule
  • Differentiation of implicit functions, Logarithmic Differentiation, Differentiation of parametric functions,

Application and Derivatives (Topic Weightage : 2 %)

  • Davisson Germer Experiment, Electron Diffraction, Nuclear Reactors, Communications, Basic Components of a Communication System, Modulation, Modulation Factor, Fax, Television Signals Propagations, Height of transmitting antenna, C.R.O Tube, Wilson Cloud Chamber,

Tangents and Normals (Topic Weightage : 1 %)

  • Slope (Gradient) of a line,

Monotonicity (Topic Weightage : 1 %)

  • Monotonic function.

Maxima Minima (Topic Weightage : 2 %)

  • Maxima and Minima, 2nd derivative, Global Maximum / Minimum, Discontinuous Function, 

Graphical Transformation (Topic Weightage : 1 %)

  • Some Standard Graphs, Straight Line, Ellipse, Hyperbola, Rectangular Hyperbola, Plotting graph of f(x – [x]),

Relations and Functions
In daily life, we cone across many relations such as Teacher and Students, Mother and Daughter Book and cost. In mathematics also, we come across many relations such as.
In this chapter, we will learn how to connect pairs of objects from two sets and then introduce relation between two objects in pair finally. we shell learn about special type of relations called functions. From the beginning of modern mathematics in the 17th century, the concept of function has been at the very centre of mathematical thoughts. It gives the mathematical rule by which one quantity corresponds to another quantity.

Limits & Derivatives
The invention of calculus was one of the most for reaching events in the history of mathematics. It is the part of mathematics which mainly deals with the study of change in the value of function as the value of the variable in the domain change. Calculus has a very wide range of uses in Sciences, Engineering, Economics and in many other walk of life. It is extensively used in graphical work including the calculation of the slope of tangent to a curve at a point.
We shall introduce the concept of limit of a real function, study some algebra of limits and will evaluate limits of some algebra and trigonometric function. The we shall define the derivatives of a real function, give its geometrical and physical interpretation. Study some algebra of derivatives and will obtain derivatives of some algebraic and trigonometric functions.

Continuity and Differentiability
The invention of calculus was one of the most for reaching events in the history of mathematics. It is that part of mathematics which mainly deals with the study of change in the value of a function as the value of the variable in the domain change. Calculus has a very wide range of uses in Science, Engineering, Economics and in many other walk of life. It is extensively used in graphical work, including the calculation of the slope of tangent to a curve at a point.
In the chapter of Continuity and Differentiability we shall introduce the concept of limit of a real function, study some algebra of limits and will evaluate limits of some algebraic and trigonometric function. Then we shall define the derivative of a real function, give its geometrical and Physical interpretation study some algebra of derivatives and will obtain derivatives of some algebraic, Trigonometric, Inverse, logarthim, Variable Rais to Power Variable, Implicit Derivatives and Double Derivatives.

In Engineering, Physics, Chemistry and sometimes in subject like Economics, Biology etc. If become necessary to build a mathematical model to represent certain problems. If is often the case that these mathematical models involve the search of the unknown function that satisfies the equation which contain the derivatives of unknown function, such equations are called Differential Equations. We can use these techniques in real life situations.

Application of Derivatives
None derivatives are widely used in various fields such as science engineering, social science etc. Here we shall separately study the Application of Derivatives in
1. Determining rate of change of quantities.
2. Finding the equations of tangents and normals to a curve at a point.
3. Finding intervals in which a give function is increasing or decreasing.
4. Finding turning points on the graph of a function
5. Finding maximum and minimum values of a function
6. Finding approximate value of a certain quantities.