The function $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 - 2x + 3{x^2} - 4{x^3} + \ldots {\rm{to}}\,\,\,\,\infty ,x \ne - 1}\\ {1,x = - 1} \end{array}} \right.$ is

Continuous and derivable at $x = - 1$

Continuous but not derivable at $x = - 1$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The function

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {1 - 2x + 3{x^2} - 4{x^3} + \ldots \mathrm{to}\,\,\,\,\infty ,x \ne - 1}\\ {1,x = - 1} \end{array}} \right.

View answer and explanation

Correct option: B

Neither continuous nor derivable at

x = - 1

Option B (Neither continuous nor derivable at

x = - 1

) is correct because the function is not defined at

x = -1

and the limit as

x

approaches

-1

is infinity, indicating a discontinuity.