jog511 said:Homework Statement
lim x->0 (2sinxcosx)/ (2x^2 + x )
Homework Equations
2sinxcosx = sin(2x)
The Attempt at a Solution
denom. factors to x(2x +1) how to proceed?
jog511 said:can it be written as sin2x/2x * 1/(x + 1/2)
jog511 said:I get lim = 2
A trigonometric limit is a mathematical concept that represents the value that a function approaches as the input variable approaches a specific value. In other words, it is the value that the function "gets close to" but never actually reaches.
Trigonometric limits are important in calculus because they help us understand the behavior of functions near specific points. They also allow us to evaluate complicated functions that cannot be solved directly.
Solving a trigonometric limit involves using various algebraic and trigonometric identities and techniques, such as factoring, rationalizing, and using the properties of limits. In some cases, a graphing calculator may also be helpful.
Some common types of trigonometric limits include limits involving sine, cosine, tangent, secant, and cotangent functions. These limits may involve various trigonometric identities, limits at infinity, or special angles.
Yes, L'Hopital's rule can be used to solve certain types of trigonometric limits. This rule states that if the limit of a function f(x)/g(x) as x approaches a specific value is an indeterminate form (such as 0/0 or ∞/∞), then the limit of the derivative of f(x) divided by the derivative of g(x) is equivalent to the original limit. However, this rule should be used with caution and may not always yield an accurate result.