Trigonometric Limits

Trigonometric Limits

more examples of limits

Substitution Theorem for

Trigonometric Functions

laws for evaluating limits

Theorem A. For each point c in function¡¯s

domain:

lim sin x = sin c,

x¡úc

lim tan x = tan c,

x¡úc

lim csc x = csc c,

x¡úc

lim cos x = cos c,

x¡úc

lim cot x = cot c,

x¡úc

lim sec x = sec c.

x¡úc

Theorem A. For each point c in function¡¯s

domain:

lim sin x = sin c,

x¡úc

lim tan x = tan c,

x¡úc

lim csc x = csc c,

x¡úc

lim cos x = cos c,

x¡úc

lim cot x = cot c,

x¡úc

lim sec x = sec c.

x¡úc

Proof. Prove first that

lim sin x = 0,

x¡ú0

lim cos x = 1.

x¡ú0

Is it obvious?

lim sin x = 0,

x¡ú0

y=sin(x)

lim cos x = 1.

x¡ú0

y=cos(x)

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