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**Something simple that i cannot visualize!?!?**

## Homework Statement

limit as x approaches 0 for sinx/4x

## Homework Equations

ok....what i know is that sinx/x=1 so by that simple statement the answer becomes 1/4 because sinx/x=1 and than there's 4x which gives me the 4....so 1/4......i tend to over think things......another question is why would cos3x=1 when x goes to 0? i know cosx goes to 1 when x equals 0.....but wouldn't you multiply 1 by 3 so it would be 3 or is it because it oscillates to 1 all the time?

## The Attempt at a Solution

ok so there's a way our teacher does it that i'm trying to figure out that way, even though i know the answer right off the bat, just thinking it might help me in the future

lim as X approaches 0 for sinx/4x.........lim as x approaches 0 for (sinx)/((4x/4)*4)....this is to get rid of the 4(or should i be multiplying by 4x?) in the 4x and to put it on the outside.......1/4 lim as x approaches 0 for (sinx)/(x).......lim as x approaches 0 for (1/4)*(1)=1/4.....look right to everyone? am i cancelling out the 4x right?

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