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Find the values of k so that the function f is continuous at the indicated point f(x)={(k cos x/π−2x, if x ≠ π/2) (3, if x = π/2)
Solution:
The given function is
f(x) = {(k cos x/π − 2x, if x ≠ π/2) (3, if x = π / 2)
The given function f is continuous at x = π / 2,
if f is defined at x = π / 2 and if the value of the f at x = π / 2 equals the limit of f at x = π / 2.
It is evident that f is defined at x = π / 2 and f(π / 2) = 3
limx→π/2 f(x) = limx→π/2 k cos x / π − 2x
Put x = π / 2 + h
Then x→π/2
⇒ h→0
⇒ limx→π/2 f(x) = limx→π/2 k cos x / π − 2x
= lim h→0 k cos(π/2 + h) / π − 2(π/2 + h)
=k lim h→0 − sin h − 2h
= k/2 lim h→0 sin h = k/2.1
= k/2
⇒ limx→π / 2 f(x) = f(π / 2)
⇒ k / 2 = 3
⇒ k = 6
Therefore, the value of k = 6
NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 26
Find the values of k so that the function f is continuous at the indicated point f(x)={(k cos x/π−2x, if x ≠ π/2) (3, if x = π/2)
Summary:
The values of k so that the function f is continuous at the indicated point f(x)={(k cos x/π−2x, if x ≠ π/2) (3, if x = π/2) is 6
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