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IGNOU MTE-01 - Calculus

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IGNOU MTE-01 Code Details

  • University IGNOU (Indira Gandhi National Open University)
  • Title Calculus
  • Language(s) English
  • Code MTE-01
  • Subject Mathematics
  • Degree(s) B.Sc.
  • Course Core Courses (CC)

IGNOU MTE-01 English Topics Covered

Block 1 - Elements of Differential Calculus

  • Unit 1 - Real Numbers and Functions
  • Unit 2 - Limits and Continuity
  • Unit 3 - Differentiation
  • Unit 4 - Derivatives of Trigonometric Functions
  • Unit 5 - Derivatives of Some Standard Functions

Block 2 - Drawing Curves

  • Unit 1 - Higher Order Derivatives
  • Unit 2 - The Ups and Downs
  • Unit 3 - Geometrical Properties of Curves
  • Unit 4 - Curve Tracing

Block 3 - Integral Calculus

  • Unit 1 - Definite Integral
  • Unit 2 - Methods of Integration
  • Unit 3 - Reduction Formulas
  • Unit 4 - Integration of Rational and Irrational Functions

Block 4 - Application of Calculus

  • Unit 1 - Applications of Differential Calculus
  • Unit 2 - Area Under a Curve
  • Unit 3 - Further Applications of Integral Calculus
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IGNOU MTE-01 (January 2023 - December 2023) Assignment Questions

IGNOU MTE-01 (January 2022 - December 2022) Assignment Questions

1. Which of the following statements are true? Justify your answers: i) If a function f from R to R is such that |f| is continuous, then f is also continuous. ii) The function f, defined by f (x) = x + sin x, is monotonic in v) y (x2 +4) = 2 has oblique asymptotes. 2. a) If is true or not. b) Find lower and upper integrals of f, defined on [−1, 1], by Hence, check the integrability of f on [−1, 1]. 3. a) Check whether the function f , defined by f(x) = cos x − cos3x, is periodic or not. b) By dividing the internal [4,0] into 4 equal parts, find the approximate value of using Simpon’s rule. c) Differentiate 4. a) If, for Hence, evaluate I2. b) Find the derivative of (tan x) sec x + (sec x) cot x with respect to x. 5. a) Trace the curve , x2 = y2 (x+1)3 stating all the properties used in the process. 6. a) State Lagrange’s Mean Value Theorem and use it to prove that b) Evaluate: 7. a) Find the volume of the solid generated by the revolution of the curve (a − x) y2 = a2 x about its asymptote. b) A function f is defined on R by Determine the value(s) of C so that f becomes continuous on R . 8. a) Find the area of one arch of the cycloid x = a(t –sin t), y = a(1 – cos t) bounded by its base. b) Evaluate c) Find the values of (0.98)5/2 upto 3 decimal places. 9. a) Find the area included between the parabolas y2 = 4x and x2 = 4y. b) If 10. a) Differentiate b) Evaluate: c) Find the equation of the tangent and the normal to the curve x2 + y2 + 4x + 3y – 25 = 0 at (-3, 4).
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