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NIMCET Previous Year Questions (PYQs)

NIMCET Continuity PYQ

Test the continuity of the function at x = 2 
$f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 & \text{ if } x=2 \\ x-\frac{3}{2}& \text{ if } x>2 \end{cases}$





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Solution

LHL ≠ f(2)
Let  ,where [x]denotes the greatest integer





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Solution

$f(x)=x+|x|$ is continuous for





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Solution

If $f\colon R\rightarrow R$ is defined by $f(x)=\begin{cases}{\frac{x+2}{{x}^2+3x+2}} & {,\, if\, x\, \in R-\{-1,-2\}} \\ {-1} & {,if\, x=-2} \\ {0} & {,if\, x=-1}\end{cases}$ , then f(x) is continuous on the set 





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Solution

 is continuous for





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Solution

If  is a continuous function at x = 0, then the value of k is





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Solution


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