Math Problem Statement
What is the limit of tan (2x) when x is approaching pi/4 from the negative
Solution
To find the limit of as approaches from the negative side, we proceed step by step.
Step 1: Substituting the limit value into
As , we have:
Step 2: Behavior of
The tangent function becomes undefined at . However, we are interested in what happens when approaches from the negative side.
- As , approaches because the tangent function tends to positive infinity when approaching from the left side.
Conclusion:
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Related Questions:
- What is the limit of as ?
- How does the tangent function behave at other critical points, like ?
- Can we generalize the behavior of trigonometric limits involving for any constant ?
- What is the limit of as ?
- How can we use series expansions to analyze the limit of near ?
Tip:
When dealing with trigonometric limits near critical points, always check whether the function tends toward infinity or negative infinity by considering which side of the point you're approaching from!
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Math Problem Analysis
Mathematical Concepts
Limits
Trigonometric Functions
Continuity
Formulas
lim_{x \to c^-} \tan(2x)
Behavior of tan(θ) as θ approaches π/2
Theorems
Limit Theorem for Trigonometric Functions
Asymptotic Behavior of Tangent Function
Suitable Grade Level
Grades 11-12
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