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Maths Avatarm
Индия
Добавлен 29 мар 2024
I have created this channel for Mathematics education. The purpose of this channel is to prepare students for Mathematics competitive exams like CSIR-NET, GATE, IIT-JAM, CUET, DSSSB-PGT, NBHM, TIFR, ISI, IISC, state-wise Assistant Professor competitive exams like UPSC, UPPSC GDC, UPHESC, BPSC, HPSC, MPPSC, JPSC and other competitive exams. Apart from the competitive exams, this channel is also useful for B.Sc. and M.Sc. students. Join us and secure your future.
I am Dr. Amit Kumar. I did Ph.D. from NISER Bhubaneswar and M.Sc. from IIT Guwahati in Mathematics. I am also CSIR UGC NET-JRF, GATE, NBHM, IIT-JAM qualified. I have three years of teaching experience.
I am Dr. Amit Kumar. I did Ph.D. from NISER Bhubaneswar and M.Sc. from IIT Guwahati in Mathematics. I am also CSIR UGC NET-JRF, GATE, NBHM, IIT-JAM qualified. I have three years of teaching experience.
If f is twice differentiable on I, then f is convex if and only if f''(x)≥0 ∀ x∈I.
In this lecture, we show that if f is twice differentiable on I, then f is convex if and only if f''(x)≥0 ∀ x∈I. @AmitKumar-cg7be
Просмотров: 29
Видео
f is convex if and only if f' is increasing
Просмотров 18День назад
In this lecture, we show that if f:I→R is a differentiable function, then f is convex if and only if f' is increasing on I. @AmitKumar-cg7be
If f is convex, then (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x).
Просмотров 26День назад
If f:I→R be a convex function, then for a,b,x∈I with a strictly less than x strictly less than b, we have (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x). @AmitKumar-cg7be
If f is a convex differentiable at x_0∈I, then f has absolute minimum at x_0 iff f'(x_0 )=0.
Просмотров 20День назад
In this lecture, we show that if f:I→R is a convex function differentiable at x_0∈I, then f has absolute minimum at x_0 if and only if f'(x_0 )=0. @AmitKumar-cg7be
If f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I.
Просмотров 22День назад
In this lecture, we show that if f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I. @AmitKumar-cg7be
For a convex function, a point of local minimum is the point of absolute minimum.
Просмотров 2814 дней назад
In this lecture, we show that for a convex function, a point of local minimum is the point of absolute minimum. @AmitKumar-cg7be
Convex functions and examples
Просмотров 2414 дней назад
In this lecture, we define convex functions and also give examples of some of convex functions. @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏.
Просмотров 1314 дней назад
In this, we determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏. @AmitKumar-cg7be
How many horizontal asymptotes can the graph of a given rational function have?
Просмотров 1214 дней назад
In this, we discuss, How many horizontal asymptotes can the graph of a given rational function have? @AmitKumar-cg7be
Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero?
Просмотров 2314 дней назад
In this, we discuss, Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero? @AmitKumar-cg7be
Let 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. What is l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) ?
Просмотров 1414 дней назад
In this, we find l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) if 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙+𝟏).
Просмотров 1221 день назад
In this, we determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙 𝟏). @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=(𝒙+𝟑)/(𝒙+𝟐).
Просмотров 821 день назад
In this, we determine all the asymptotes of the curve 𝒚=(𝒙 𝟑)/(𝒙 𝟐). @AmitKumar-cg7be .
Determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑).
Просмотров 1621 день назад
In this, we determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑). @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=√𝒙+𝟒/√(𝒙+𝟒).
Просмотров 1021 день назад
In this, we determine all the asymptotes of the curve 𝒚=√𝒙 𝟒/√(𝒙 𝟒). @AmitKumar-cg7be
Determine all the asymptotes of the curve y=(1-x^2)/(x^2+1).
Просмотров 2621 день назад
Determine all the asymptotes of the curve y=(1-x^2)/(x^2 1).
Determine all the asymptotes of the curve y=(x^2+4)/(x-3).
Просмотров 1421 день назад
Determine all the asymptotes of the curve y=(x^2 4)/(x-3).
Determine all the asymptotes of the curve y=(x^2+x-6)/(x^2+2x-8).
Просмотров 921 день назад
Determine all the asymptotes of the curve y=(x^2 x-6)/(x^2 2x-8).
Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 1721 день назад
Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 5021 день назад
Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 2221 день назад
Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Asymptotes of a curve given in polar form
Просмотров 2221 день назад
Asymptotes of a curve given in polar form
Asymptotes of a curve given in parametric form
Просмотров 1328 дней назад
Asymptotes of a curve given in parametric form
Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)
Просмотров 2228 дней назад
Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)
Definition of Asymptotes of Curves and its types
Просмотров 27Месяц назад
Definition of Asymptotes of Curves and its types
f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.
Просмотров 13Месяц назад
f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.
If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.
Просмотров 15Месяц назад
If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.
f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)
Просмотров 22Месяц назад
f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)
f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)
Просмотров 46Месяц назад
f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)
cosx strictly less than (sinx/x)^3 for all x∈(0, π/2)
Просмотров 24Месяц назад
cosx strictly less than (sinx/x)^3 for all x∈(0, π/2)
Nice 🎉
Thanks 😅
🎉😊👍
🎉🎉nice 😊
Nice 🎉
👍👍👍
In this lecture, also add that S' is convex subset.
Good question 🎉👍
Also add in posibility (1) that neither vertical nor oblique asymptotes exists.
ALMAA HII KAAFII HAIN...😂😂😂
Good 🎉👍
Good 🎉
Nice class sir 🎉
Nice class 🎉😊
Samjhne me problem ho ta hai
Sir sound proper nahi aata hai
Nice class 😊 🎉
Good 🎉 👍
Nice class ❤🎉
Good 👍👍👍
Nice 🎉
Nice class 👍
Nice class 🎉😊
Good
Nice class
Hello Sir, could you please make a video on how to prove that the total number of subgroups of dihedral group is τ(n) + σ(n)
SUC 2 mei jo problem likha hai uska answer to btake jao..😂😂
Good question 👍
keep it up
Nice 🎉
Good 👍
More videos
More videos
🙏
Nice class 🎉❤
Love from nit delhi electrical❤
Nice class 🎉😊
Nice explanation 🎉
🙏
Nice class 😊
Thanks for the class sir Nice class 🎉🎉❤
Nice class ❤
Nice class sir 🎉😊 Thanks for the class 🙏
Good class 😊🎉
👍👍😊
In group G, read a^2=b^2=c^2=-I instead of a^2=b^2=c^2=I.
@@AmitKumar-cg7be Hello Sir, could you please make a video on how to prove that the total number of subgroups of dihedral group is τ(n) + σ(n)
I will make.
❤
🎉❤😊
Nice class ❤
Nice class sir ji😊🎉