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29 votes
29 votes
Find a so the function be continuous Function

Find a so the function be continuous Function-example-1
User Palaniraja
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2 Answers

12 votes
12 votes

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
User Abhishek Maurya
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3.2k points
11 votes
11 votes

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

User Gregwhitaker
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2.4k points