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TIFR-2011-Maths-B-4

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3 votes
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1
makhdoom ghaya asked Dec 9, 2015
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TIFR-2011-Maths-A-25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.
The function$f(x)= \begin{cases}0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$is not continuous anywhere on the real line.
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1 votes
1 votes
1 answer
2
makhdoom ghaya asked Dec 9, 2015
577 views
TIFR-2011-Maths-A-21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
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1 votes
1 votes
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3
makhdoom ghaya asked Dec 9, 2015
1,557 views
TIFR-2011-Maths-A-14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
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1 votes
1 votes
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4
makhdoom ghaya asked Dec 9, 2015
587 views
TIFR-2011-Maths-A-19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$ at $x = 1$ is $e^{-1}$ .
The derivative of the function$\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$at $x = 1$ is $e^{-1}$ .
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