Question

Question 5. Is the function f defined by f(x)=
_fx, if x 51
con tinuous
at x = 0? At x = 1? At x = 2 ?​

Answer 1

Answer:

Definition of continuity at x = a

$f(a) = \lim_{x \to {a}^{ + } }(f(a)) = \lim_{x \to {a}^{ - } }(f(a))$

You can easily check that function is continuous at x = 0 and x = 2

Now at x = 1

$f(1) = 1 \\ \lim_{x \to {1}^{ + } }(f(x)) = 5 \\ 1 \: \neq \: 5$

So function has discontinuity at x = 1

Answer 2

Answer:

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