Question

Need help with this
Lim (sin2x+tan3x)/x when x->0+
Result = 5

Answer 1

sen? or sin?

Answer 2

sin, sorry

Answer 3

\[\frac{\sin 2x+\tan 3x}{x}\]

Answer 4

yeah

Answer 5

\[\frac{\sin 2x}{x} + \frac{\tan 3x}{x}\]

Answer 6

\[\frac{2\sin 2x}{2x} + \frac{3 \tan 3x}{3x}\]

Answer 7

\[\lim_{x \rightarrow 0} \frac{sinx}{x} =1\]

Answer 8

\[\tan x = \frac{\sin x}{\cos x}\]

Answer 9

\[2\frac{\sin 2x }{x} + \frac{3}{\cos{3x}} \frac{\sin 3x}{3x}\]

Answer 10

crap i made a typoooooo

Answer 11

pretend its divided by 2x instead of x

Answer 12

\[\frac{\sin 2x+\tan 3x}{x} = 2 \frac{\sin 2x}{2x} + \frac{3}{\cos 3x} \frac{\sin 3x}{3x}\]

Answer 13

so, can you do the limit now?
\[\lim_{x \rightarrow 0^+} 2 \frac{\sin 2x}{2x} + \frac{3}{\cos 3x}\frac{\sin 3x}{3x}\]

Answer 14

3/ 3cos(0) = 3/3 = 1 ?

Answer 15

2+3 = 5 ?

Answer 16

the lim of sin 2x /2x is 1

the lim of sin 3x/ 3x is 1

the lim of 3/ cos 3x = 3/1 = 3

Answer 17

its 3/ cos 3x not 3/3cos3x

Answer 18

and then yes, 2+3 = 5

Answer 19

OHHH, sorry. I am a lil bit sleepy. Thank you so much. You saved my life

Answer 20

when in doubt, see if any trig identities will make the problem easier

Answer 21

Thank you so muuuuch. I hope you are having a great night <3