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f-x-sin-x-e-x-1-Prove-that-f-x-has-only-2-zeros-in-pi-x-0-

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Question Number 211637 by CrispyXYZ last updated on 15/Sep/24
f(x) = sin x − e^x + 1. Prove that f(x) has only 2 zeros in −π≤x≤0.
f(x)=sinx−ex+1.Provethatf(x)hasonly2zerosin−π⩽x⩽0.
Answered by mehdee1342 last updated on 15/Sep/24
f(0)=0 f(−π)=1−e^(−π) 0 & f(−(π/2))=−e^(−(π/2)) <0 ⇒∃ −π<a<−(π/2) ; f(a)=0
f(0)=0f(−π)=1−e−π0&f(−π2)=−e−π2<0⇒∃−π<a<−π2;f(a)=0

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