Chapter 12
Inverse Trigonometric Functions,
Hyperbolic Functions, and
L’Hôpital’s Rule
T
his chapter looks at the very important inverse trigonometric functions and the
hyperbolic functions. For these functions, you see lots of examples related to finding
derivatives and integration as well. Although you don’t spend much time on the hyperbolic
functions in most calculus courses, the inverse trigonometric functions come up again
and again; the inverse tangent function is especially important when you tackle the partial
fraction problems of Chapter 14. At the end of this chapter, you experience a blast from the
past: limit problems!
The Problems You’ll Work On
This chapter has a variety of limit, derivative, and integration problems. Here’s what you
work on:
✓ Finding derivatives and antiderivatives using inverse trigonometric functions
✓ Finding derivatives and antiderivatives using hyperbolic functions
✓ Using L’Hôpital’s rule to evaluate limits
What to Watch Out For
Here are a few things to consider for the problems in this chapter:
✓ The derivative questions just involve new formulas; the power, product, quotient, and
chain rules still apply.
✓ Know the definitions of the hyperbolic functions so that if you forget any formulas, you
can easily derive them. They’re simply defined in terms of the exponential function, e
x
.
✓ Although L’Hôpital’s rule is great for many limit problems, make sure you have an
indeterminate form before you use it, or you can get some very incorrect solutions.
Inverse Trigonometric Functions,
Hyperbolic Functions, and
L’Hôpital’s Rule
T
his chapter looks at the very important inverse trigonometric functions and the
hyperbolic functions. For these functions, you see lots of examples related to finding
derivatives and integration as well. Although you don’t spend much time on the hyperbolic
functions in most calculus courses, the inverse trigonometric functions come up again
and again; the inverse tangent function is especially important when you tackle the partial
fraction problems of Chapter 14. At the end of this chapter, you experience a blast from the
past: limit problems!
The Problems You’ll Work On
This chapter has a variety of limit, derivative, and integration problems. Here’s what you
work on:
✓ Finding derivatives and antiderivatives using inverse trigonometric functions
✓ Finding derivatives and antiderivatives using hyperbolic functions
✓ Using L’Hôpital’s rule to evaluate limits
What to Watch Out For
Here are a few things to consider for the problems in this chapter:
✓ The derivative questions just involve new formulas; the power, product, quotient, and
chain rules still apply.
✓ Know the definitions of the hyperbolic functions so that if you forget any formulas, you
can easily derive them. They’re simply defined in terms of the exponential function, e
x
.
✓ Although L’Hôpital’s rule is great for many limit problems, make sure you have an
indeterminate form before you use it, or you can get some very incorrect solutions.