Ex 5.1, 27 Find k so that f(x) = {kx2 , 3 is continuous at x = 2 - Ex 5.1

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Ex 5.1, 27 Find the values of k so that the function f is continuous at the indicated point 𝑓 𝑥﷯= 𝑘𝑥2 , 𝑖𝑓 𝑥≤2﷮3, 𝑖𝑓 𝑥>2﷯﷯ at x = 2 Given that function is continuous at 𝑥 = 2 𝑓 is continuous at 𝑥 = 2 if L.H.L = R.H.L = 𝑓 2﷯ i.e. lim﷮x→ 2﷮−﷯﷯ 𝑓 𝑥﷯= lim﷮x→ 2﷮+﷯﷯ 𝑓(𝑥)= 𝑓 2﷯ i.e. lim﷮x→ 2﷮−﷯﷯ 𝑓 𝑥﷯= lim﷮x→ 2﷮+﷯﷯ 𝑓(𝑥)=𝑘 2﷯﷮2﷯ i.e. lim﷮x→ 2﷮−﷯﷯ 𝑓 𝑥﷯= lim﷮x→ 2﷮+﷯﷯ 𝑓(𝑥)=4𝑘 Since LHL = RHL ⇒ 4k = 3 ⇒ k = 𝟑﷮𝟒﷯

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