Question

Find a so the function be continuous Function

Answer 1

The answer is a = 3.

Finding Left Hand Limit (LHL)

`\displaystyle \lim_(x \to \11^(-)) f(x) = -2(1) + a`

Finding Right Hand Limit (RHL)

`\displaystyle \lim_(x \to \11^(+)) f(x) = 1`

For a continuous function, LHL = RHL

• -2 + a = 1
• a = 3

Answer 2

The limit as x approaches 1 from either side should match, so that

`\displaystyle\lim_(x\to1^-)f(x)=\lim_(x\to1)(-2x+a)=a-2`

`\displaystyle\lim_(x\to1^+)f(x)=\lim_(x\to1)x=1`

==> a - 2 = 1 ==> a = 3