powp said:sorry I get 0.05575
A limit is a mathematical concept that describes the behavior of a function as the input approaches a particular value. It can be thought of as the value that a function is approaching, but not necessarily reaching, as the input gets closer and closer to a certain point.
To evaluate a limit, you must first substitute the given value into the function. Then, you must simplify the resulting expression as much as possible. If the resulting expression is undefined at the given value, you must use additional techniques such as factoring, algebraic manipulation, or trigonometric identities to rewrite the expression in a form that allows for further simplification. Finally, you take the resulting value as the limit.
Evaluating a limit at a specific value means finding the limit of a function as the input approaches that particular value. This is typically denoted as "lim x→a f(x)", where "a" is the value at which the limit is being evaluated. It is important to note that the function may or may not actually attain the value at "a", but rather the limit represents the behavior of the function as the input gets closer and closer to "a".
To evaluate the limit of a trigonometric function, you must use trigonometric identities to manipulate the expression into a form that allows for further simplification. For example, in the given problem of evaluating "sin(x + sinx) at x=π", you can use the double angle formula for sine to rewrite the expression as "sinx(cosx+1)". Then, you can substitute "π" for "x" and continue simplifying until you reach a final value for the limit.
The limit of sin(x + sinx) at x=π is equal to 1. This can be found by following the steps mentioned in the previous question, using the double angle formula for sine and substituting "π" for "x". The final expression will simplify to "sinπ(cosπ+1)", and since "sinπ = 0" and "cosπ = -1", the limit becomes "0(-1+1) = 0". Therefore, the limit of sin(x + sinx) at x=π is equal to 1.