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SPECIAL TRIG LIMITS EXAMPLES

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

limx0sinxx=1limx0cosx - 1x=0limx0tanxx=1

Evaluate the following limits :

Problem 1 :

limx03sinxx

Solution :

limx03sinxxlimx0sinxx=3(1)= 3

Problem 2 :

limx02cos x - 2x

Solution :

limx02cos x - 2xlimx0cos x - 1x

Problem 3 :

limx0sinx4x

Solution :

limx0sinx4xlimx0sin xx

Problem 4 :

limx0sin7xx

Solution :

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

limx0sin7xxlimx0sin 7xxlimx0sin 7x7x

Problem 5 :

limx0sin 3x2x

Solution :

limx0sin 3x2xlimx0sin 3x2xlimx0sin 3xxlimx0sin 3xxlimx0sin 3x3x

Problem 6 :

limx0xsin x

Solution :

limx0xsin xlimx01xsin xlimx0 1limx0 xsin x11

Problem 7 :

limx0-tan 2xx

Solution :

limx0-tan 2xxlimx0-tan 2xxlimx0tan 2x2x

Problem 8 :

limx0sin xx 1x

Solution :

limx0sin xx 1xlimx0sin xxlimx0 1x

Problem 9 :

limx0x-3+ sin 2xx

Solution :

limx0x-3+ sin 2xxlimx0(x-3)+limx0 sin 2xxlimx0(x-3)+limx0 sin 2xxlimx0(x-3)+2 limx0 sin 2x2x
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