ShmoopTube

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Thank you We sneak and here's your shmoop du jour

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brought to you by diagrams not the preferred method of

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birth control All right consider the following diagram The picture

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is of a wedge of a circle with a radius

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of one The angle is acts which is measured in

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radiance Because of this the arc length is also x

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A right triangle is created And the height of the

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leg next to the ark of the circle is a

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sign of acts Imagine what happens His ex gets smaller

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and smaller Smaller It appears that the height of the

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leg of the triangle and the are calling becomes indistinguishable

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Or that as x approaches zero ex becomes sign of

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acts Therefore the limit as x approaches zero signings over

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x is equal Tio what And here the potential anthony

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All right for this problem we should think of the

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division in sine x over acts as the ratio between

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sign of x and x don't worry reason we'll be

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able to get rid of that car waken See that

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as angle x gets smaller and smaller the two legs

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of the triangle get closer and closer in sign of

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ex gets smaller and smaller waken See that arc link

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with acts also gets smaller If x gets really small

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we see that the ark in vertical get closer and

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closer to each other until there nearly identical once Acts

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become 0 They do become identical and the ratio between

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the two is just one to one Therefore his ex

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approaches Zero sign of ex overact approaches one on our

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answer be

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