limits | Mathematics | Page 1

lethal bluff Jan 22, 2024, 1:16 AM

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Please help me on how to do this

void oceanBOT Jan 22, 2024, 1:16 AM

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lethal bluff Please help me on how to do this

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radiant isle Jan 22, 2024, 1:31 AM

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use the hint... break the sine !! then break the fraction and each limit will be easy

lethal bluff Jan 22, 2024, 1:35 AM

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Break the sin?

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I can do it by deriving it to cos but I don’t know how to do the hint

radiant isle Jan 22, 2024, 1:45 AM

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sin(π/6 + Δχ)=sin(π/6) cosΔχ + cos(π/6) sinΔχ

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thats how you use the hint

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you take π/6 as θ and Δx as φ

lethal bluff Jan 22, 2024, 1:48 AM

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What do I do from there tho?

radiant isle Jan 22, 2024, 1:52 AM

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you break the fraction

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@lethal bluff do you want me to tell you what to break it into

lethal bluff Jan 22, 2024, 1:57 AM

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Yes I don’t know how

radiant isle Jan 22, 2024, 1:57 AM

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$lets see if i can use this thing$

pine lavaBOT Jan 22, 2024, 1:57 AM

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mintago

radiant isle Jan 22, 2024, 1:58 AM

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hmm

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$[sin(π/6) cosΔχ + cos(π/6) sinΔχ - 1/2 ]/Δx$

pine lavaBOT Jan 22, 2024, 1:58 AM

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mintago
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radiant isle Jan 22, 2024, 1:58 AM

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dark it

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n

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ok nevermind

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[sin(π/6) cosΔx + cos(π/6) sinΔχ - 1/2 ]/Δx

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you have this fraction

lethal bluff Jan 22, 2024, 1:59 AM

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Yes

radiant isle Jan 22, 2024, 1:59 AM

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break into these 2

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cos(π/6)sinΔx /Δx + (sin(π/6)cosΔx - 1/2)/Δx

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since sin(π/6) is 1/2 you can factor it out from the second fraction

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and then youll have both basic trig limits

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sinx/x and (cosx-1)/x

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and if you dont remember those just do a quick l'hospital in your head

lethal bluff Jan 22, 2024, 2:06 AM

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radiant isle Jan 22, 2024, 2:07 AM

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factor out the 1/2

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and it will be the basic limit

lethal bluff Jan 22, 2024, 2:11 AM

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Wdym

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Factor out the - 1/2 ?

radiant isle Jan 22, 2024, 2:13 AM

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make the fraction (1/2) (cosΔx-1)/Δx

lethal bluff Jan 22, 2024, 2:16 AM

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Ohhh

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So putting in 0 it s just 0 plus square root of 3 over 2

radiant isle Jan 22, 2024, 2:17 AM

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and then it just cancels out

radiant isle Jan 22, 2024, 2:17 AM

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lethal bluff So putting in 0 it s just 0 plus square root of 3 over 2

uHh

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not sure what you mean

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but thats the reult of the limit yes

lethal bluff Jan 22, 2024, 2:17 AM

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radiant isle Jan 22, 2024, 2:19 AM

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yep

lethal bluff Jan 22, 2024, 2:19 AM

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Ty so much!

radiant isle Jan 22, 2024, 2:19 AM

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np

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@lethal bluff btw

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just a tiny thing

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you forgot to put the Δ in the last fraction

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with the cos

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