Using the limit definition of a derivative, find the derivative of f(r) = r² - r. Show that this civative can also be obtained by evaluating f(r+ Ar) – f(r – Ar) lim Ar-0 2Ar

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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[5] Using the limit definition of a derivative, find the derivative of f(x) = x² – x. Show that this
derivative can also be obtained by evaluating
f(r+ A¤) – f (x – Ar)
lim
Ar-0
2Δε
Explain why you were able to get the same derivative of f (x) by describing the geometric interpretation
of this formulation of the derivative. You can draw graphs to help you discuss this.
Transcribed Image Text:[5] Using the limit definition of a derivative, find the derivative of f(x) = x² – x. Show that this derivative can also be obtained by evaluating f(r+ A¤) – f (x – Ar) lim Ar-0 2Δε Explain why you were able to get the same derivative of f (x) by describing the geometric interpretation of this formulation of the derivative. You can draw graphs to help you discuss this.
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