2.5 Continuity8540. lim sin 0 cot 200- 0sin 3y cot 5y42. limy cot 4yy00 cot 4044. lim sin? e cot 2046. lim Cos2rx2COS xa f(x) and lim,a f(x) at an interior pointdo you then know lima f(x)? Give reasonsX-f(x) exists at an interior point of a domainfind its value by calculating lim, f(x)CX-answer.Doag lnowinsth

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Asked Sep 24, 2019
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#44 

finding one sided limits algebraically 

2.5 Continuity
85
40. lim sin 0 cot 20
0- 0
sin 3y cot 5y
42. lim
y cot 4y
y0
0 cot 40
44. lim sin? e cot 20
46. lim Cos2r
x2
COS x
a f(x) and lim,a f(x) at an interior point
do you then know lima f(x)? Give reasons
X-
f(x) exists at an interior point of a domain
find its value by calculating lim, f(x)
C
X-
answer.
Doag lnowinsth
help_outline

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2.5 Continuity 85 40. lim sin 0 cot 20 0- 0 sin 3y cot 5y 42. lim y cot 4y y0 0 cot 40 44. lim sin? e cot 20 46. lim Cos2r x2 COS x a f(x) and lim,a f(x) at an interior point do you then know lima f(x)? Give reasons X- f(x) exists at an interior point of a domain find its value by calculating lim, f(x) C X- answer. Doag lnowinsth

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Expert Answer

Step 1

We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.

Express cot using sin and cos. 

lim sin 0 cot 20
00
cos 2e
= lim sin 0
sin 20
00
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lim sin 0 cot 20 00 cos 2e = lim sin 0 sin 20 00

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Step 2

Use the double angle formula for sin(2theta)

Sin(2 theta...

cos 20
im sin
sin 20
00
cos 20
lim sin
2sin cos
= lim cos 20
0-0 2cos 0
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cos 20 im sin sin 20 00 cos 20 lim sin 2sin cos = lim cos 20 0-0 2cos 0

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