domyy said:Homework Statement
lim 2x/(sin3x)
x-> 0
Homework Equations
lim sinx/x = 1
x->0
The Attempt at a Solution
is it correct to say the following:
lim 2/3 (sinx/x)
x-> 0
lim 2/3 (1)
x-> 0
Answer: lim 2x/sin3x = 2/3
x-> 0
Because it's on the book:
cos 2x(2)/3 = 2/3
x->0
So I want to know if I solve it the way I did before, would it be correct?
A limit of a trigonometric function is the value that a function approaches as its input (x-value) approaches a specific value. It is denoted by the notation "lim f(x) as x approaches a".
The limit of a trigonometric function can be calculated using algebraic techniques, such as factoring or simplifying. It can also be calculated using the rules of limits, such as the sum, product, and quotient rules.
The common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions relate the angles of a triangle to the lengths of its sides.
Yes, the limit of a trigonometric function can be undefined if the function has a vertical asymptote or if the function oscillates infinitely as x approaches a certain value.
Limits of trigonometric functions are important because they allow us to understand the behavior of these functions at certain points and to make predictions about their values. They also play a crucial role in calculus and other areas of mathematics.