Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Jan. 3, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Transcript
Ex 5.1, 4 Prove that the function f (x) = π₯^π is continuous at x = n, where n is a positive integer. Let π(π₯) = π₯^π We need to prove that π(π₯) = π₯^π is continuous at x = n π is continuous at x = n if limβ¬(xβπ) π(π₯)= π(π) limβ¬(xβπ) π(π₯) = limβ¬(xβπ) π₯^π Putting π₯=π = π^π π(π₯) = π₯^π π(π) = π^π β΄ Thus limβ¬(xβπ) f(x) = f(n) Hence, f(x) = xn is continuous at x = n
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