What is the value of the expression below? 3^4 + 9
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Answer:
Expanding f(t)f(t) around xx gives f(t)=f(x)+(t−x)f′(x)+(t−x)22f′′(τ)f(t)=f(x)+(t−x)f′(x)+(t−x)22f″(τ), where ττ lies between tt and xx.
For t=0t=0 this gives 0=f(0)=f(x)−xf′(x)+x22f′′(θx)0=f(0)=f(x)−xf′(x)+x22f″(θx) with θ∈(0,1)θ∈(0,1) and therefore f′(x)−f(x)x=x2f′′(θx)f′(x)−f(x)x=x2f″(θx).
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Answer:
90
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