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mathslover Group TitleBest ResponseYou've already chosen the best response.0
It is easy , it just looks long. I will do that after lunch, ok?
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Huge \lim_{x \rightarrow 0}( \frac{1}{x} \int\limits_{0}^{a} e^{\sin^{2}t}dt\int\limits_{x+y}^{a} e^{\sin^{2}t}dt)\]
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
Okay @mathslover and I know it is easy,I was trying it but i think the first term will cancel off because a and y both are constants maybe..i can be wrong,just drop a hint.
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
sorry the term 1/x is outside everything
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
we can write the expression as.... (first term) + ∫ e^(sin^2 t dt) with limits ... a to x+y.. the sign changed on reversing the limits..
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
now combining the two limits.. 0 to a and a to x+y .. 0 to x+y ..
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
because the integrand is same..
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
0 to a and 0 to x+y=0 to x+y
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Huge \frac{1}{x} e^{\sin^{2}x+y}\]
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
differenatiate and bingo :O
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
why did you not do anything to 1/x ?
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
multiplication theorem.. hmm..
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
1/x was outside the integral sorry :P
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
aur jab 0 put krenge.. to bhi to kuch aayega. vo kahan gyi? :P
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
Wait.Lets start again :
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Huge \lim_{x \rightarrow 0} \frac{1}{x}(\int\limits_{y}^{a}e^{\sin^{2}t} dt\int\limits_{x+y}^{a}e^{\sin^{2}t} dt)\]
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
original question^
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Large \lim_{x \rightarrow 0} \frac{1}{x}(\int\limits_{y}^{x+y}e^{\sin^{2}t} dt)\] On changing the sign and revevrsing the limits and combining them
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
acha vo 'a' vala to 0 ho jayega.. a ki differentiation 0.. but hamne x+y ko differentiate bhi nhi kra.. :/
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
@shubhamsrg ?? :)
 one year ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
kya hua? kya dikkat hai ? (:
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Huge e^{\sin^{2}{x+y}}(1+\frac{dy}{dx})e^{\sin^{2}y} \frac{dy}{dx}\]
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
why put dy/dx=0 ?
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\Huge e^{\sin^{2}x+y}\] answer
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
y is behaving as a constant,we assume y independent of x
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
idk what i wrote please someone explain :P
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
ohhh.. achaaaa..
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
If we are driving a car and chasing a thief on a bike then the rate of change of our speed won't affect the speed of the theif's bike
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
limit y se x+y ?? how??
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
tune he to bataya?:/
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
i said 0 to x+y.. :/
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
wo "A" hai 0 nahi :
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
but still didnt get it :
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\LARGE e^{\sin^{2}x+y}\] differentiating this^
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\LARGE e^{\sin^{2}x+y} \times \sin2x(+0)\]
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\LARGE e^{\sin^{2}y}\] Differentiating the lower limit^
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
\[\LARGE e^{\sin^{2}y}=>e^{\sin^{2}y} \times \sin2y\]
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
lower limit will become 0
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
I'm left with.. \[\LARGE \frac{1}{x}e^{\sin^{2}x+y} \times \sin2x\]
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
abbe yr. x ki differentiation 1 hogi.. LH me numerator aur denominator alag alag diff krte hain.. :/
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
maine bhi to wahi bola tha BC
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
to x ki diff 1 ho jayegi.. aur numerator me tune jo kra tha. dy/dx=0 krke aa jayega ans.
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
kya 1 ka 0? 1 baari diff krenge.. :/
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
1/x hai to 1 ka karenge to 0 x ka karenge to 1 0/1=0
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
lol. 1*x ki diff. 0*x + 1*1.. lol
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
to upar sirf 1 thodi hai.. baaki bhi to hai. usse multiply krega saara.. to 1* ....... = ......... aa jayega.. :O
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
par sin2x kahan gaya?
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
main question :P
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
newton lebinitz me integrand ki differentiation nhi krte.. limits ko integrand me daalte hain multiply by limits ki diff..
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal :*
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.1
seekho @shubhamsrg
 one year ago

yrelhan4 Group TitleBest ResponseYou've already chosen the best response.2
lol. meri bezti badi achi krte ho aap log. :/
 one year ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
maine upar kuch padha bhi nahi kya likha hai :3
 one year ago

knock Group TitleBest ResponseYou've already chosen the best response.0
What's the answer then? xD
 one year ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
@yrelhan4 is the answer to all the questions . O:)
 one year ago

knock Group TitleBest ResponseYou've already chosen the best response.0
Great xD I thought in a way to solve it but if it's already solved then ok (:
 one year ago
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