IGNOU MTE 3 2018 - Which of the following statements are true? Give reasons for your answ

Question

Which of the following statements are true? Give reasons for your answers.

i) The derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions.

ii) The function of f ( x) = sin x/2 + sinx has a maxima at x = π/2 .

iii) 2x + 3 y + 4z = 0 represents a line in 3-dimenisonal space.

v) In a Binomial distribution if mean is known then standard deviation is also known.

v) If two events are mutually exclusive then they are independent.

02 Feb 2018

Answer :

Word Count : 399

Let's go through each statement one by one:

i) The derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions.
- True. This statement is true, and it is known as the quotient rule in calculus. If you have a function h(x) defined as the quotient of two functions, h(x) = f(x)/g(x), then the derivative of h(x) is h'(x) = (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2.

ii) The function f(x) = sin(x/2) + sin(x)

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