Find the values of k so that the function f is continuous at the indicated point. f(x) = {(k x², if x ≤ 2) (3, if x > 2)

Solution:

The given function is

f(x) = {(k x², if x ≤ 2) (3, if x > 2)

The given function f is continuous at x = 2,

if f is defined at x = 2 and if the value of the f at x = 2 equals the limit of f at x = 2.

It is evident that f is defined at x = 2 and f(2) = k(2)² = 4k.

 limx→2^- f(x) = limx→2⁺ f(x) = f(2)

⇒ limx→2^- (k x²) = limx→2⁺ (3)

= 4k

⇒ k × 2² = 3 = 4k

⇒ 4k = 3

⇒ k = 3/4

Therefore, the value of k = 3/4

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NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 27

Find the values of k so that the function f is continuous at the indicated point. f(x) = {(k x², if x ≤2) (3, if x > 2)

Summary:

The value of k so that the function f is continuous at the indicated point. f(x) = {(k x², if x ≤2) (3, if x > 2) is 3/4