For what value of lambdais the function defined by f(x)={{:(lambd | Filo
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Class 12

Math

Calculus

Continuity and Differentiability

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For what value of is the function defined by continuous at ? What about continuity at ?

Solution: Solution: to be continuous at ,


which is not true.
So, is not continuots at .
Now, at ,
\displaystyle\Lim_{{{x}\to{1}}}{f{{\left({x}\right)}}}=\Lim_{{{x}\to{1}}}{4}{x}+{1}={5}={f{{\left({1}\right)}}}
Therefore, is continuous at .
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