Trig Limits Using Double Angle Identity Notes | York University - Edubirdie

University:
York University
Course:
MATH 1013 | Applied Calculus I
Academic year:

2022
Views:

370

Pages:

1
Author:

Nick T.

Trig Limits Using Double Angle Identity lim (1-cos2x)/(2x^2) = lim (2sin^2x)/(2x^2) = lim (sin^2x)/(x^2) = 1 Trigonometric Limits lim (1-cosθ)/(θ) = 0 lim (sinθ)/(θ) = 1 Squeeze Theorem (Sandwich Theorem): Finding Limits lim(x→0) (1-cos x)/(x) * (1+cos x)/(1+cos x) = lim(x→0) (sin^2 x)/(x(1+cos x)) = 0 lim(x→5) (3x)/(x^2-5x) = lim(x→5) 3/(x-5) = 3/0 = ∞ lim(x→5) (√(x+4) - 3)/(x-5) * (√(x+4) + 3)/(√(x+4) + 3) = 1/(√(x+4) + 3) = 1/6 lim(x→-2) (6x^2+11x+12)/(x^2-4) = 6(x+1)/(x-2) = -1/6

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