Видео 760
Просмотров 708 403

An Alternative Definition of ln(x): the limit of 2^n(xn - 1) and 2^n(1 - 1/xn) (ILIEKMATHPHYSICS)

30:14

Prove that lim n(x^1/n - 1) = ln(x) (ILIEKMATHPHYSICS)

5:46

Prove if x ﹥ 0, then lim(x^1/n) = 1 (Second Proof) (ILIEKMATHPHYSICS)

5:46

Prove if x ﹥ 0, then lim(x^1/n) = 1 (First Proof) (ILIEKMATHPHYSICS)

4:09

Prove the limit of sin(x) / x = 1 as x approaches 0 (ILIEKMATHPHYSICS)

20:21

Prove that sin(x) / cos(x) = tan(x) (ILIEKMATHPHYSICS)

12:02

Geometric Explanation of arctan x = lim(2^n xn) = lim(2^n xn / sqrt(1+xn^2)) (ILIEKMATHPHYSICS)

This video is part of the “Real Analysis” series I am making.
Thanks and enjoy the video!
Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS
Note that this video is not a proof that the sequences converge to arctan x. The purpose here is to give a geometric perspective of what the two sequences look like.
Proof that 2^n xn converges video: ruclips.net/video/41mHRdnpp7o/видео.html
Proof that 2^n xn / sqrt(1+xn^2) converges video: ruclips.net/video/seEyryvLOJk/видео.html

Видео

An Alternative Definition of ln(x): the limit of 2^n(xn - 1) and 2^n(1 - 1/xn) (ILIEKMATHPHYSICS)

30:14

An Alternative Definition of ln(x): the limit of 2^n(xn - 1) and 2^n(1 - 1/xn) (ILIEKMATHPHYSICS)

Просмотров 5084 часа назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Proof of limit of n(x^1/n - 1) = ln(x) video: ruclips.net/video/96z-uCrq7LA/видео.html Link to Hurwitz's paper: ia600708.us.archive.org/view_archive.php?archive=/28/items/crossref-pre-1923-scholarly-works/10.1007%2Fbf01449600.zip&file...

Prove that lim n(x^1/n - 1) = ln(x) (ILIEKMATHPHYSICS)

5:46

Prove that lim n(x^1/n - 1) = ln(x) (ILIEKMATHPHYSICS)

Просмотров 3,1 тыс.7 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS

Prove if x ﹥ 0, then lim(x^1/n) = 1 (Second Proof) (ILIEKMATHPHYSICS)

5:46

Prove if x ﹥ 0, then lim(x^1/n) = 1 (Second Proof) (ILIEKMATHPHYSICS)

Просмотров 8679 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS

Prove if x ﹥ 0, then lim(x^1/n) = 1 (First Proof) (ILIEKMATHPHYSICS)

4:09

Prove if x ﹥ 0, then lim(x^1/n) = 1 (First Proof) (ILIEKMATHPHYSICS)

Просмотров 3969 часов назад

Prove the limit of sin(x) / x = 1 as x approaches 0 (ILIEKMATHPHYSICS)

20:21

Prove the limit of sin(x) / x = 1 as x approaches 0 (ILIEKMATHPHYSICS)

Просмотров 1,7 тыс.12 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that 2^n xn converges (definition of arctan) video: ruclips.net/video/41mHRdnpp7o/видео.html Prove if x ﹥ 0, then x/sqrt(1 x^2) ﹤ arctan(x) video: ruclips.net/video/seEyryvLOJk/видео.html Prove that |arctan x| = arctan|x| video ...

Prove that sin(x) / cos(x) = tan(x) (ILIEKMATHPHYSICS)

12:02

Prove that sin(x) / cos(x) = tan(x) (ILIEKMATHPHYSICS)

Просмотров 1,6 тыс.14 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that e^z * e^w = e^(z w) video: ruclips.net/video/PK0JxSVo7oE/видео.html Proof that 2^n xn converges (definition of arctan) video: ruclips.net/video/41mHRdnpp7o/видео.html Prove that arctan is bounded (definition of pi) video: r...

Prove that cos(x) is decreasing on [0,π] (ILIEKMATHPHYSICS)

8:03

Prove that cos(x) is decreasing on [0,π] (ILIEKMATHPHYSICS)

Просмотров 59314 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that sin2x - sin2y = 2sin(x-y)cos(x y) and cos2x - cos2y = -2sin(x-y)sin(x y) video: ruclips.net/video/XZh2EGS7Xxg/видео.html Prove that cos(x) ﹥ 0 for all x in -π/2 ﹤ x ﹤ π/2 video: ruclips.net/video/wXIwDQSwTHc/видео.html Last...

Prove that cos(x) ﹥ 0 for all x in -π/2 ﹤ x ﹤ π/2 (ILIEKMATHPHYSICS)

7:03

Prove that cos(x) ﹥ 0 for all x in -π/2 ﹤ x ﹤ π/2 (ILIEKMATHPHYSICS)

Просмотров 63116 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that 2^n xn converges (definition of arctan) video: ruclips.net/video/41mHRdnpp7o/видео.html Prove that arctan : R → (-π/2, π/2) is onto video: ruclips.net/video/A45bHcz1zH4/видео.html Prove that arctan(1) = π/4 video: ruclips.n...

What is sin(nπ/2) = ? and cos(nπ/2) = ? (ILIEKMATHPHYSICS)

12:45

What is sin(nπ/2) = ? and cos(nπ/2) = ? (ILIEKMATHPHYSICS)

Просмотров 28716 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Video containing proof of cos(π/2) = 0 and sin(π/2) = 1: ruclips.net/video/bKa8yU5L-KA/видео.html Proof of De Moivre's Theorem video: ruclips.net/video/7nKKfWLdvnI/видео.html

Prove De Moivre's Theorem (cosz + isinz)^k = coskz + isinkz (ILIEKMATHPHYSICS)

8:23

Prove De Moivre's Theorem (cosz + isinz)^k = coskz + isinkz (ILIEKMATHPHYSICS)

Просмотров 1 тыс.19 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Proof that cosine is even and sine is odd video: ruclips.net/video/Zea-Yf3FVbk/видео.html Prove the sine and cosine addition formulas video: ruclips.net/video/tOAmJkv3YWE/видео.html Prove that sin^2(z) cos^2(z) = 1 video: ruclips.net/...

Prove that sin(x) and cos(x) are continuous (ILIEKMATHPHYSICS)

9:41

Prove that sin(x) and cos(x) are continuous (ILIEKMATHPHYSICS)

Просмотров 1,1 тыс.19 часов назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that |sin(x)| ≤ 1 and |cos(x)| ≤ 1 video: ruclips.net/video/9lpPcf-ic6M/видео.html Prove that |sin(x)| ≤ |x| video: ruclips.net/video/UeQqg17pDHU/видео.html Prove that sin2x - sin2y = 2sin(x-y)cos(x y) and cos2x - cos2y = -2sin(...

Prove that sin2x - sin2y = 2sin(x-y)cos(x+y) and cos2x - cos2y = -2sin(x-y)sin(x+y)

4:25

Prove that sin2x - sin2y = 2sin(x-y)cos(x+y) and cos2x - cos2y = -2sin(x-y)sin(x+y)

Просмотров 18321 час назад

Prove that |sin x| ≤ |x| (ILIEKMATHPHYSICS)

13:34

Prove that |sin x| ≤ |x| (ILIEKMATHPHYSICS)

Просмотров 2,2 тыс.21 час назад

Prove that cos(2arctanx) = 1-x^2 / 1+x^2 and sin(2arctanx) = 2x / 1+x^2 (ILIEKMATHPHYSICS)

6:01

Prove that cos(2arctanx) = 1-x^2 / 1+x^2 and sin(2arctanx) = 2x / 1+x^2 (ILIEKMATHPHYSICS)

Просмотров 309День назад

This video is part of the “Real Analysis” series I am making. Thanks and enjoy the video! Real Analysis Playlist: ruclips.net/p/PLDiddIbnOEOWLbdQ4DoC8bfaV_y4VyOsS Prove that 2^n xn converges (definition of arctan) video: ruclips.net/video/41mHRdnpp7o/видео.html Prove that e^2iarctanx = 1 ix / 1-ix video: ruclips.net/video/9vzCYkw_oFs/видео.html Prove that cos(x) = Re(e^ix) and sin(x) = Im(e^ix)...

Prove that |sin x| ≤ 1 and |cos x| ≤ 1 (ILIEKMATHPHYSICS)

4:34

Prove that |sin x| ≤ 1 and |cos x| ≤ 1 (ILIEKMATHPHYSICS)

Просмотров 1,5 тыс.День назад

Prove that |sin x| ≤ 1 and |cos x| ≤ 1 (ILIEKMATHPHYSICS)

Prove that sin^2(z) + cos^2(z) = 1 (ILIEKMATHPHYSICS)

2:55

Prove that sin^2(z) + cos^2(z) = 1 (ILIEKMATHPHYSICS)

Просмотров 319День назад

Prove that sin^2(z) cos^2(z) = 1 (ILIEKMATHPHYSICS)

Prove the sine and cosine addition formulas for complex numbers (ILIEKMATHPHYSICS)

8:07

Prove the sine and cosine addition formulas for complex numbers (ILIEKMATHPHYSICS)

Просмотров 395День назад

Prove the sine and cosine addition formulas for complex numbers (ILIEKMATHPHYSICS)

Prove that cos(-z) = cos(z) and sin(-z) = -sin(z) (ILIEKMATHPHYSICS) (cos is even and sine is odd)

3:17

Prove that cos(-z) = cos(z) and sin(-z) = -sin(z) (ILIEKMATHPHYSICS) (cos is even and sine is odd)

Просмотров 673День назад

Prove that cos(-z) = cos(z) and sin(-z) = -sin(z) (ILIEKMATHPHYSICS) (cos is even and sine is odd)

Prove Euler's Formula e^iz = cos(z) + isin(z) (ILIEKMATHPHYSICS)

2:09

Prove Euler's Formula e^iz = cos(z) + isin(z) (ILIEKMATHPHYSICS)

Просмотров 569День назад

Prove Euler's Formula e^iz = cos(z) isin(z) (ILIEKMATHPHYSICS)

Prove that cos(x) = Re(e^ix) and sin(x) = Im(e^ix) (ILIEKMATHPHYSICS)

4:32

Prove that cos(x) = Re(e^ix) and sin(x) = Im(e^ix) (ILIEKMATHPHYSICS)

Просмотров 461День назад

Prove that cos(x) = Re(e^ix) and sin(x) = Im(e^ix) (ILIEKMATHPHYSICS)

Prove that the conjugate of e^z is equal to e^conjugate of z (ILIEKMATHPHYSICS)

5:06

Prove that the conjugate of e^z is equal to e^conjugate of z (ILIEKMATHPHYSICS)

Просмотров 493День назад

Prove that the conjugate of e^z is equal to e^conjugate of z (ILIEKMATHPHYSICS)

Prove if zn converges to z, then zn conjugate converges to z conjugate (ILIEKMATHPHYSICS)

4:38

Prove if zn converges to z, then zn conjugate converges to z conjugate (ILIEKMATHPHYSICS)

Просмотров 19814 дней назад

Prove if zn converges to z, then zn conjugate converges to z conjugate (ILIEKMATHPHYSICS)

Prove that arctan(1) = π/4 (ILIEKMATHPHYSICS) (Real Analysis)

16:45

Prove that arctan(1) = π/4 (ILIEKMATHPHYSICS) (Real Analysis)

Просмотров 92014 дней назад

Prove that arctan(1) = π/4 (ILIEKMATHPHYSICS) (Real Analysis)

Prove that arctan : R → (-π/2, π/2) is onto (ILIEKMATHPHYSICS) (definition of tan(x))

13:01

Prove that arctan : R → (-π/2, π/2) is onto (ILIEKMATHPHYSICS) (definition of tan(x))

Просмотров 33314 дней назад

Prove that arctan : R → (-π/2, π/2) is onto (ILIEKMATHPHYSICS) (definition of tan(x))

Prove that lim{x→∞} arctan(x) = π/2 and lim{x→-∞} arctan(x) = -π/2 (ILIEKMATHPHYSICS)

10:24

Prove that lim{x→∞} arctan(x) = π/2 and lim{x→-∞} arctan(x) = -π/2 (ILIEKMATHPHYSICS)

Просмотров 41514 дней назад

Prove that lim{x→∞} arctan(x) = π/2 and lim{x→-∞} arctan(x) = -π/2 (ILIEKMATHPHYSICS)

Prove that arctan(x) is bounded (ILIEKMATHPHYSICS) (includes a definition of pi)

13:23

Prove that arctan(x) is bounded (ILIEKMATHPHYSICS) (includes a definition of pi)

Просмотров 34814 дней назад

Prove that arctan(x) is bounded (ILIEKMATHPHYSICS) (includes a definition of pi)

Prove that arctan(x) is continuous (ILIEKMATHPHYSICS)

13:43

Prove that arctan(x) is continuous (ILIEKMATHPHYSICS)

Просмотров 48714 дней назад

Prove that arctan(x) is continuous (ILIEKMATHPHYSICS)

arctan(x) is an increasing function (Proof) (ILIEKMATHPHYSICS)

5:56

arctan(x) is an increasing function (Proof) (ILIEKMATHPHYSICS)

Просмотров 49614 дней назад

arctan(x) is an increasing function (Proof) (ILIEKMATHPHYSICS)

If xy ﹤ 1, then arctan(x) + arctan(y) = arctan((x+y)/(1-xy)) (Proof) (ILIEKMATHPHYSICS)

17:29

If xy ﹤ 1, then arctan(x) + arctan(y) = arctan((x+y)/(1-xy)) (Proof) (ILIEKMATHPHYSICS)

Просмотров 37114 дней назад

If xy ﹤ 1, then arctan(x) arctan(y) = arctan((x y)/(1-xy)) (Proof) (ILIEKMATHPHYSICS)