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If  is continuous at x = 0, then k = ?

Answer (Detailed Solution Below)

Option 4 :
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Detailed Solution

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Concept:

Definition:

  • A function f(x) is said to be continuous at a point x = a in its domain, if  exists or or if its graph is a single unbroken curve at that point.
  • f(x) is continuous at x = a ⇔ .

 

Formulae:

 

Calculation: 

Since f(x) is given to be continuous at x = 0, .

Also,  because f(x) is same for x > 0 and x < 0.

 

.

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