AP Calculus – Evaluate More Limits | Direct Substitution of Roots, Rational, and Trig Functions

Описание: In this episode of the Limit Series, we evaluate four different types of limits:
• Radical functions (Problem 5)
• Rational expressions (Problem 8)
• Trigonometric functions (Problems 9 and 10)

Step by step, we substitute and simplify to find each limit. This video shows how limits apply to square roots, rational functions, sine, and cosine.

[Key Concepts]
• Direct substitution for limits when functions are continuous
• Evaluating radical functions: √x behavior near a point
• Rational function limits with fractions
• Trigonometric limits involving sin(x) and cos(x)
• Substitution at specific points (x → 3, -3/2, π, 3π/4)

[Study Tip]
When solving limit problems:
1. Always try direct substitution first. For radicals, carefully simplify the square root.
3. For rational functions, reduce step by step before substituting.
4. Remember special trig values: sin(π) = 0, cos(3π/4) = -√2/2.

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