SPECIAL TRIG LIMITS EXAMPLES

There are three special trigonometric limits rules that we must know. We will learn more about these techniques in calculus.

limx→0sinxx=1limx→0cosx - 1x=0limx→0tanxx=1

Evaluate the following limits :

Problem 1 :

limx→03sinxx

Solution :

limx→03sinxxlimx→0sinxx=3(1)= 3

Problem 2 :

limx→02cos x - 2x

Solution :

limx→02cos x - 2xlimx→0cos x - 1x

Problem 3 :

limx→0sinx4x

Solution :

limx→0sinx4xlimx→0sin xx

Problem 4 :

limx→0sin7xx

Solution :

To get the form sin ax/a, we should multiply the numerator and denominator by a.

limx→0sin7xxlimx→0sin 7xxlimx→0sin 7x7x

Problem 5 :

limx→0sin 3x2x

Solution :

limx→0sin 3x2xlimx→0sin 3x2xlimx→0sin 3xxlimx→0sin 3xxlimx→0sin 3x3x

Problem 6 :

limx→0xsin x

Solution :

limx→0xsin xlimx→01xsin xlimx→0 1limx→0 xsin x11

Problem 7 :

limx→0-tan 2xx

Solution :

limx→0-tan 2xxlimx→0-tan 2xxlimx→0tan 2x2x

Problem 8 :

limx→0sin xx⋅ 1x

Solution :

limx→0sin xx⋅ 1xlimx→0sin xx⋅limx→0 1x⋅

Problem 9 :

limx→0x-3+ sin 2xx

Solution :

limx→0x-3+ sin 2xxlimx→0(x-3)+limx→0 sin 2xxlimx→0(x-3)+limx→0 sin 2xxlimx→0(x-3)+2 limx→0 sin 2x2x

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