EVALUATING LIMITS SPECIAL TRIGONOMETRIC FUNCTIONS
There are three special trigonometric limits rules that we must know. We will learn more about these techniques in calculus.
Evaluate the following limits. Show all work.
Problem 1 :
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Problem 2 :
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Problem 3 :
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Problem 4 :
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Problem 5 :
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Problem 6 :
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Problem 7 :
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Problem 8 :
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Problem 9 :
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Problem 10 :
Solution :
Given, x ⇾ 0- sin xx + 1x= x ⇾ 0- sin xx + x ⇾ 0- 1x= 1 + (-∞)= -∞
Problem 11 :
x ⇾ 0 x sin 7x x
Solution :
Given, x ⇾ 0 x sin 7x xMultiplying and dividing by 7.= 7 x ⇾ 0 x sin 7x 7x= 7 (0)= 0
Problem 12 :
x ⇾ 0 3x + sin 3xx
Solution :
Given,x ⇾ 0 3x + sin 3xx= x ⇾ 0 3x + x ⇾ 0 sin 3xxx ⇾ 0 sin 3xxMultiplying and dividing by 3.=3 x ⇾ 0 sin 3x3x= 3 3x ⇾ 0 sin 3x3x= 3(1) = 3= 0 + 3= 3