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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,

# Compute the limit of the given function

Evaluate the limit.

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

# Compute the limit of the given function

Evaluate the limit.

First,

Then, we multiply inside the limit by since ,

# Compute the limit of the given function

Evaluate the limit.

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

Using this we compute,

# Compute the limit of the given function

Evaluate the limit.

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

# Compute the limit of the given function

Evaluate the limit.

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

# Compute the limit of the given function

Evaluate the limit.

Let , then as and we have

# Compute the limit of the given function

Evaluate the limit.

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

Then we have

# Compute the limit of the given function

Evaluate the limit.

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

# Compute the limit of the given function

Evaluate the limit.

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