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Test 1: Calculus

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1) If $f(x)$ is derivable in the interval $[a-h, a+h]$, prove that

(i) f(a+h)f(ah)=h[f(a+θ1h)+f(aθ1h)], where 0<θ1<1

(ii) f(a+h)2f(a)+f(ah)=h[f(a+θ2h)f(aθ2h)], where 0<θ2<1


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