Check the continuity of the function f(x) = \(\begin{cases}x & \quad

1.	Check the continuity of the function f(x) = \(\begin{cases}x & \quad \text{if } x ≤ 1 \text{ }\\5 & \quad \text{if } x > 1 \text{}\end{cases}\)at x = 1.
Answer» At x = 1, L.H.L = 1 R.H.L = 5 L.H.L ≠ R.H.L, so f(x) is discontinuous at x = 1

Check the continuity of the function f(x) = \(\begin{cases}x & \quad \text{if } x ≤ 1 \text{ }\\5 & \quad \text{if } x > 1 \text{}\end{cases}\)at x = 1.

Answer»

At x = 1,

L.H.L = 1

R.H.L = 5

L.H.L ≠ R.H.L, so f(x) is discontinuous at x = 1

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Check the continuity of the function f(x) = \(\begin{cases}x &amp; \quad \text{if } x ≤ 1 \text{ }\\5 &amp; \quad \text{if } x &gt; 1 \text{}\end{cases}\)at x = 1.

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Check the continuity of the function f(x) = \(\begin{cases}x & \quad \text{if } x ≤ 1 \text{ }\\5 & \quad \text{if } x > 1 \text{}\end{cases}\)at x = 1.