Limits diffrent method confirmation

The 2nd image is giving answer the 3rd one is giving 0 is it all correct?
Also how does a single limit have diffrent values?

iTeachChem Helper•7/23/25, 2:50 PM

@Apu

iTeachChem Helper•7/23/25, 2:50 PM

Note for OP

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wilted_flowerOP•7/23/25, 2:51 PM

,rotate

TeXit•7/23/25, 2:51 PM

An unexpected internal error occurred while running your command! Please report the following error to the developer:

discord.errors.DiscordServerError: 503 Service Unavailable (error code: 0): upstream connect error or disconnect/reset before headers. reset reason: overflow

discord.errors.DiscordServerError: 503 Service Unavailable (error code: 0): upstream connect error or disconnect/reset before headers. reset reason: overflow

wilted_flowerOP•7/23/25, 2:58 PM

Welp

wilted_flowerOP•7/23/25, 4:30 PM

, rotate

TeXit•7/23/25, 4:30 PM

wilted_flowerOP•7/23/25, 4:30 PM

It's this correct?

CorrodedCoffin•7/23/25, 5:27 PM

yaar aana toh zero hi chahiye

CorrodedCoffin•7/23/25, 5:27 PM

something fishy is going on

Prasan•7/23/25, 5:36 PM

haan kara to theek hai

wilted_flowerOP•7/23/25, 6:55 PM

2nd is the marked answer and wo bhi galat nahi hai

wilted_flowerOP•7/23/25, 6:55 PM

but 0 bhi sahi hai

wilted_flowerOP•7/23/25, 6:56 PM

diff approaches diffrent limit value??

CorrodedCoffin•7/23/25, 7:45 PM

graph se toh 1/2 hi aayea

Wwilted_flower The 2nd image is giving answer the 3rd one is giving 0 is it all correct? Also h...

SirLancelotDuLac•7/24/25, 1:55 AM

Nuh uh. A limit can't give 2 values (unless it doesn't exist). The approximation taken in the third one is incomplete. Since the denominator is of x⁴, we have to take into consideration all the terms of x until the power of 4 (which means the second term in expansion of tanx is to be taken)

SirLancelotDuLac•7/24/25, 1:56 AM

(Tldr: Approximation sahi se lena is very important in limits, especially when 0 by 0 kinda stuff)

wilted_flowerOP•7/24/25, 2:53 AM

wait what

wilted_flowerOP•7/24/25, 2:53 AM

damn

SSirLancelotDuLac Nuh uh. A limit can't give 2 values (unless it doesn't exist). The approximation...

Prasan•7/24/25, 12:06 PM

but in some other questions when we did this, there wasnt any problem in that. uska bataoge

PPrasan but in some other questions when we did this, there wasnt any problem in that. u...

SirLancelotDuLac•7/24/25, 12:30 PM

Kyunki there first degree approximation worked. For example Ek hai (tanx-sinx)/x^3. Isme first degree approximation isliye nahi laga sakte kyunki expansion ke x^3 wale terms are significant w.r.t denominator and hence bring a change about the result.

SirLancelotDuLac•7/24/25, 12:30 PM

Similarly if the question was (tanx-sinx)/x^2, now the first degree approximation would work since the second terms of expansion (the x^3 terms) are much smaller w.r.t. denominator (x^2)

SSirLancelotDuLac Kyunki there first degree approximation worked. For example Ek hai (tanx-sinx)/x...

Prasan•7/24/25, 1:23 PM

Yar vo significant ka kya mtlb ga, significant wrt drnominator

wilted_flowerOP•7/24/25, 1:48 PM

I get it okk

wilted_flowerOP•7/24/25, 1:49 PM

Goes back to how these were derived in the first place

wilted_flowerOP•7/25/25, 3:43 AM

fine fine sorted ig

wilted_flowerOP•7/25/25, 3:43 AM

+solved @SirLancelotDuLac

iTeachChem Helper•7/25/25, 3:43 AM

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Limits diffrent method confirmation

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