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51 votes
51 votes

Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE?

  1. $f$ is continuous in $[-1, 1]$
  2. $f$ is not bounded in $[-1, 1]$
  3. $A$ is nonzero and finite
  1. II only
  2. III only
  3. II and III only
  4. I, II and III
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7 Answers

4 votes
4 votes
Option a .Draw the graph and yes area and integration are not same.Integration will be 0 area will be infinite in this case and its not bounded in -1to1
3 votes
3 votes
a function f(x) is continuous at the closed interval or bounded only if:

f(x) is continuous for all values of x in the interval (a,b) and

f(x) is right continuous at f(a)

 and left continuous at f(b).

In the above question f(0) doesn't exist hence the function is not bounded in the closed interval [a,b]. So its definitely not a bounded function.

Hope that answers the doubt on how to know whether a function is bounded or not.
–3 votes
–3 votes
ye kiske paper mein tha? this is not there in the 2015 CS paper? any of the sets.

if....somebody could provide the answer by IITK please
Answer:

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