# Homework Help: Is this the same as lim x→2 sin(x)?

1. Feb 29, 2016

### AllanW

1. The problem statement, all variables and given/known data
if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places

2. Relevant equations
(f(x+h)-f(x))/h

3. The attempt at a solution
On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91

2. Feb 29, 2016

### Staff: Mentor

No, the limit at the top is not the same as sin(2).

3. Feb 29, 2016

### Ray Vickson

Instead of "guessing" and remaining uncertain, try evaluating $(f(2+h)-f(2))/h$ numerically for a few small values of $h$, such as $h = 1/2,\, 1/4,\, 1/8, \ldots,$ etc. That way, you can answer your question for yourself and you will furthermore understand much better what is happening.

Last edited: Feb 29, 2016
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