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This particular Assignment references the syllabus chosen for the subject of Mathematics, for the January 2023 - December 2023 session. The code for the assignment is MTE-01 and it is often used by students who are enrolled in the B.Sc. Degree.
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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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