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2.4.31sin 0Use the relation lim=1 to determine the limit,0 012x12x cos (12x)imx0 sin (12x) cos (12x)Select the correct answer below and, if necessary, fill in the answer box to complete your choice.O A. im12x+12x cos (12x)(Simplify your answer.)(12x)x+0 sin (12x) cosOB. The limit does not exist.

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2.4.31
sin 0
Use the relation lim
=1 to determine the limit,
0 0
12x12x cos (12x)
im
x0 sin (12x) cos (12x)
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
O A. im12x+12x cos (12x)
(Simplify your answer.)
(12x)
x+0 sin (12x) cos
OB. The limit does not exist.
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2.4.31 sin 0 Use the relation lim =1 to determine the limit, 0 0 12x12x cos (12x) im x0 sin (12x) cos (12x) Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. im12x+12x cos (12x) (Simplify your answer.) (12x) x+0 sin (12x) cos OB. The limit does not exist.

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check_circleAnswer
Step 1

Given,

...
lim 12x+12x cos (12x)
x0 sin(12x)cos (12x)
lim 12x(1+cos(12x))
x0 sin(12x)cos (12x)
2cos2 (x))
(1+
cos2x
12x (2 cos2 (6x))
2
x0 2 x sin(12x)cos (12x)
(2sinxcosx
lm
sin2x)
lim 48x x cos2(6x)
sin(24x)
x0
Since, Lim sin(0)
00
1
sin (24x)
1
lim
x0
e
2 cos2(6x)
24x
1X
2
= 2
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lim 12x+12x cos (12x) x0 sin(12x)cos (12x) lim 12x(1+cos(12x)) x0 sin(12x)cos (12x) 2cos2 (x)) (1+ cos2x 12x (2 cos2 (6x)) 2 x0 2 x sin(12x)cos (12x) (2sinxcosx lm sin2x) lim 48x x cos2(6x) sin(24x) x0 Since, Lim sin(0) 00 1 sin (24x) 1 lim x0 e 2 cos2(6x) 24x 1X 2 = 2

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Tagged in

Math

Calculus

Limits

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