Let a,c be nonnegative real numbers and let f:[a,b]→[c,d] be a bijective increasing function. Prove that there is a unique real number μ∈(a,b) such that within limits a to b ∫f(t)dt=(μ−a)c+(b−μ)d. Bhaiya... please explain the solution for this question.
No..it should be option d Explanation: x = e satisfies the equation when a = 2...and after x = e, the function is increasing, so it cannot have a root in (e, infinity)👍
@@abhyam_6996 If you have prepared well, analysed your mocks properly, then why will your rank not boost?✨... Don't feel demotivated, this time is crucial ❤️
absolutely underrated
Gold🎉Thank you sir😊
hey brotha happy to see u help aspirants like me, also pls continue this in english, cuz it will be very helpful for non hindi speakers like me :)
Sure✨...stay tuned with us.
Prove that the Legendre polynomial
F^n (x)=d^ny/dx (1−x2)^n
has n
distinct real roots between (-1,1) using LMVT theorem?
Thank u sir 🙏🙏
tq sir
Let a,c
be nonnegative real numbers and let f:[a,b]→[c,d]
be a bijective increasing function. Prove that there is a unique real number μ∈(a,b)
such that within limits a to b
∫f(t)dt=(μ−a)c+(b−μ)d.
Bhaiya... please explain the solution for this question.
Thank you sirr
Continue your short cut series
In how many ways can 4 identical apples and 4 identical oranges can distributed among 6 children if each child gets at least 1 fruit?
In q4 what how did you calculate area of 'a' directly? Is there a formula for it?
quarter ellise - triangle
It is the double of the smaller area bounded by ellipse and the straight line passing through the ends of major and minor axis✨
Thank you sir
Very creative problems
Thx sir
But in last case you only counted polygons with even sides then how can you generalize
The probability in case of a odd polygon will be zero as you will not find any other "diametrically oposite" vertex of the polygon 👍
@MathemagixJEE
Okay thanks I just missed that part in rush
1Q answer should be option C because a can’t be equal to 2
No..it should be option d
Explanation:
x = e satisfies the equation when a = 2...and after x = e, the function is increasing, so it cannot have a root in (e, infinity)👍
A could be equal to 2 bro why not it mqy some integral roots but it wont be in thw e to infinity
Thank you sir❤
My exam on 29th shift 2
@RahilPatel1808 All the best ✨
My exam on 28th shift 1
@-Anubhav All the best ✨👍
Thank you
@@MathemagixJEE thanks
Nice👍
Did you make them all
Yes, I derived them from the memory based papers of JM Jan attempt ✨
@@MathemagixJEEloved the problems sir
give me ur brain I will get 100 in math😂love your calculation speed
My rank will not boost😞
@@abhyam_6996 If you have prepared well, analysed your mocks properly, then why will your rank not boost?✨... Don't feel demotivated, this time is crucial ❤️
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