Find the values of k so that the function f is continuous at the indicated point f(x) = {(k x + 1, if x ≤ π) (cos x, if x > π) at x = π

Solution:

The given function is

f(x) = {(k x + 1, if x ≤ π) (cos x, if x > π)

The given function f is continuous at x = π,

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

It is evident that f is defined at x = π and f(π) = kπ + 1

 lim_x→π⁻ f(x) = lim_x→π⁺ f(x) = f(π)

⇒ lim_x→π⁻ (k x + 1) = lim_x→π⁺ (cos x)

= kπ + 1

⇒ kπ + 1 = cos π

= −1

= kπ + 1 = -1

⇒ k = −2/π

Therefore, the value of k = −2/π

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NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 28

Find the values of k so that the function f is continuous at the indicated point f(x) = {(k x + 1, if x ≤ π) (cos x, if x > π) at x = π

Summary:

The value of k so that the function f is continuous at the indicated point f(x) = {(k x + 1, if x ≤ π) (cos x, if x > π) at x = π is −2/π