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Explain why the limitslimh0fx+h-fxhandlimzxfz-fxz-xare the same for any function f. (Hint: Consider the substitution z=x+h.)

Short Answer

Expert verified

limh0fx+h-fxhand limzxfz-fxz-xare the same for any functionf.

Step by step solution

01

Step 1. Given information

We have to prove that limh0fx+h-fxhand role="math" localid="1648378255156" limzxfz-fxz-xare the same for any functionf.

02

Step 2. Proof of the question

Substitute z=x+h

When zx, the value of h0

limzxfz-fxz-x=limh0fx+h-fxx+h-x=limh0fx+h-fxh

Hence it is proved.

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