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A day full of math games & activities. Find one near you.
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
limx→π− f(x) = limx→π+ f(x) = f(π)
⇒ limx→π− (k x + 1) = limx→π+ (cos x)
= kπ + 1
⇒ kπ + 1 = cos π
= −1
= kπ + 1 = -1
⇒ k = −2/π
Therefore, the value of k = −2/π
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
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