SPECIAL TRIG LIMITS EXAMPLES
There are three special trigonometric limits rules that we must know. We will learn more about these techniques in calculus.
Evaluate the following limits :
Problem 1 :
Solution :
Problem 2 :
Solution :
Problem 3 :
Solution :
Problem 4 :
Solution :
To get the form sin ax/a, we should multiply the numerator and denominator by a.
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