Are you familiar with Taylor series ?mtayab1994 said:Homework Statement
solve the following limit: [tex]\lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}[/tex]
The Attempt at a Solution
I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to separate it then solve but i don't know. Any help on how to start please?
mtayab1994 said:No haven't learned it can you fill me on it please?
SammyS said:Are you familiar with Taylor series ?
mtayab1994 said:ok i counted and found the limit to be -2 is that correct?
Dick said:Yes, if you used l'Hopital then you might check whether that is allowed. Otherwise you should try doing it using that the limit of sin(x)/x is 1.
A trigonometric limit is a mathematical concept used to describe the behavior of a function as the input values approach a certain value. In other words, it is the value that a function approaches as the input values get closer and closer to a specific value.
To solve a trigonometric limit, you must use a combination of algebraic manipulations and trigonometric identities to simplify the expression and then apply the limit laws to evaluate the limit.
Some common trigonometric identities used to solve limits include the Pythagorean identities, sum and difference identities, and double angle identities.
The main steps in solving a trigonometric limit include identifying the type of limit (finite or infinite), simplifying the expression using trigonometric identities, applying limit laws, and evaluating the limit.
Yes, there are a few special cases to consider when solving trigonometric limits, such as limits involving indeterminate forms (such as 0/0 or ∞/∞) and limits involving trigonometric functions with irrational or undefined values (such as sin(π/2) or tan(π)). In these cases, additional techniques such as L'Hôpital's rule or trigonometric substitutions may be necessary to solve the limit.