- #1

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## Homework Statement

If f(x) = sin x, evaluate

lim f(2+h) - f(2) / h

h->0

Evaluate to 2 decimal places

## Homework Equations

## The Attempt at a Solution

I think that since f(2) then the answer is sin 2 which is .91

What do you guys think?

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- Thread starter meeklobraca
- Start date

- #1

- 189

- 0

If f(x) = sin x, evaluate

lim f(2+h) - f(2) / h

h->0

Evaluate to 2 decimal places

I think that since f(2) then the answer is sin 2 which is .91

What do you guys think?

- #2

danago

Gold Member

- 1,122

- 4

## Homework Statement

If f(x) = sin x, evaluate

lim f(2+h) - f(2) / h

h->0

Evaluate to 2 decimal places

## Homework Equations

## The Attempt at a Solution

I think that since f(2) then the answer is sin 2 which is .91

What do you guys think?

If it said lim sin(h) as h->2, then the answer would be sin 2 since sin(x) is continuous.

However, the limit expression is not sin(x), it is f(2+h) - f(2) / h as h->0. Does this limit look familiar? What does it define?

- #3

HallsofIvy

Science Advisor

Homework Helper

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[tex]\frac{sin(2+h)- sin(2)}{h}[/tex] and see how small h has to be to so that you get the same answer to 2 decimal places?

- #4

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- 0

- #5

HallsofIvy

Science Advisor

Homework Helper

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What I meant was, since sin(2)= 0.9093,

Taking h= 0.1, (f(2+h)- f(2))/h= (sin(2.1)- sin(2))/.1= -.4609.

Taking h= 0.01, (f(2+h)- f(2))/h= (sin(2.01)- sin(2))/.01= -.4206

Taking h= 0.001, (f(2+h)- f(2))/h= (sin(2.001)- sin(2))/.001= -.4166

Taking h= 0.0001, (f(2+h)- f(2))/h= (sin(2.0001)- sin(2))/.0001= -.4162

- #6

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Thanks for your help!

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