Evaluate the limit.

First, we multiply and divide by the conjugate of the expression, then simplify and take the limit,

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Stumbling Robot

A Fraction of a Dot
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Tag: L’Hopital’s Rule

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

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Compute the limit of the given function

Evaluate the limit.

First, we multiply and divide by the conjugate of the expression, then simplify and take the limit,

Evaluate the limit.

First, we make the substitution . Then as so we have

Evaluate the limit.

First,

Then, we multiply inside the limit by since ,

Evaluate the limit.

We recall the definition of the hyperbolic cosine in terms of the exponential,

Using this we compute,

Evaluate the limit.

Both the numerator and denominator go to 0 as so we apply L’Hopital’s rule,

Evaluate the limit.

We use the trig identity and then use L’Hopital’s rule to evaluate,

Evaluate the limit.

Let , then as and we have

Evaluate the limit.

First, we pull an out of and an out of to write

Then we have

Evaluate the limit.

We write and apply L’Hopital’s rule to solve

Evaluate the limit.

Let , then as . Making this substitution and using L’Hopital’s rule we have