True False[1 Marks ]

Question 11 Mark

State True or False for the statements:
The composition of two continuous function is a continuous function.

Answer

True.
Solution:
The composition of two continuous functions is also a continuous function.

Question 21 Mark

State True or False for the statements:
If f is continuous on its domain D, then |f| is also continuous on D.

Answer

True.
Solution:
If a function is continuous on its domain, then the modulus of the function is also continuous in the same domain.
Hence, |f| is also continuous on D.

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Question 31 Mark

State True or False for the statements:
Rolle’s theorem is applicable for the function f(x) = |x - 1| in [0, 2].

Answer

False.
Solution:
Hence, f(x) = |x - 1| in [0, 2]. is not differentiable at $\text{x}=1\in(0,2).2$

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Question 41 Mark

State True or False for the statements:
Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

Answer

True.
Solution:
All the trigonometric and inverse trigonometric functions are differentiable in their respective domain.

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Question 51 Mark

State True or False for the statements:
If f.g is continuous at x = a, then f and g are separately continuous at x = a.

Answer

False.
Solution:
Let $\text{f(x)}=\sin\text{x}$ and $\text{g(x)}=\cot\text{x}$
$\therefore\ \text{f(x)}\cdot\text{g(x)}=\sin\cdot\frac{\cos\text{x}}{\sin\text{x}}=\cos\text{x}$
which is continuous at x = 0 but cot x is not continuous at x = 0

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Maths True False[1 Marks ]

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