- #1
Mejiera
- 15
- 0
Homework Statement
lim x appraoches 0 sin(x)/(x+tan(x))
Homework Equations
I have tryed everthing. Can someone show me how to do this.
The key to solving a trigonometric limit question is to recognize common trigonometric identities and apply them appropriately. This may involve converting trigonometric functions using identities such as sin^2x + cos^2x = 1 or using the double angle identities, among others. It is important to practice and become familiar with these identities in order to determine which one to use.
The first step in solving a trigonometric limit question is to use algebraic manipulation or trigonometric identities to simplify the expression. This may involve factoring, expanding, or using identities to rewrite the expression in a more manageable form.
A trigonometric limit question is indeterminate if it involves the ratio of two functions that both approach zero, or if it involves functions that approach infinity or negative infinity. These types of limit questions require additional steps to solve, such as using L'Hopital's rule or manipulating the expression to make it more manageable.
While a calculator may be helpful in checking your work, it is important to show your steps and understanding of the concepts when solving a trigonometric limit question. In most cases, you will not be allowed to use a calculator on a test or exam, so it is important to practice solving these questions by hand.
You can check your solution by graphing the original function and your simplified expression on a graphing calculator. If the two graphs approach the same value as x approaches the given limit, then your solution is likely correct. You can also plug in a few values of x near the limit to see if your solution matches the output of the original function.