Home » L'Hopital's Rule » Page 2

# 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 