Is this the same as lim x→2 sin(x)?

[AllanW]

Homework Statement

if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places

Homework Equations

(f(x+h)-f(x))/h

The Attempt at a Solution

On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91

 

[Mark44]

Homework Statement

if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places

Homework Equations

(f(x+h)-f(x))/h

The Attempt at a Solution

On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91

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

 

[Ray Vickson]

Homework Statement

if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places

Homework Equations

(f(x+h)-f(x))/h

The Attempt at a Solution

On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91

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.