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103/1000, a calculus problem without using calculus

• bprp calculus b… 오래 전 2026.08.18 16:00 인기
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@neilgerace355 　오래 전

Radius 5, point is (-3,4), so I thought of the 3-4-5 special right triangle.

2026-08-18 19:04

[ytcid:UgwsaKkYEKySeFeqN4Z4AaABAg] Radius 5, point is (-3,4), so I thought of the 3-4-5 special right triangle.



@bio_nerd_genev… 　오래 전

For anyone who want to know why the triangle that emerges from the radius and tangent line's relationship are always a right triangle, I recommend reading up on Thales's theorem.

2026-08-18 18:58

[ytcid:UgzJ6BkKvNwWGzyFhFN4AaABAg] For anyone who want to know why the triangle that emerges from the radius and tangent line's relationship are always a right triangle, I recommend reading up on Thales's theorem.



@MisterJackTheA… 　오래 전

But what if i wanted to use calculus?

2026-08-18 18:33

[ytcid:UgyujfXHT2A9jKJ8yZB4AaABAg] But what if i wanted to use calculus?



@vikramrawat526… 　오래 전

Day 103

2026-08-18 18:06

[ytcid:UgyfSJOI9eSfW3C-dNt4AaABAg] Day 103



@謝主隆恩 　오래 전

1. By using a simple Implicit Differentiation method, we can get that y’ = -x/y.
2. Or we can use polar coordinate system, set x = r cos theta, y = r sin theta, so y’(x) = y’(theta)/x’(theta) = x/(-y) as well.

2026-08-18 16:39

[ytcid:UgwDZBxiqVtMIGXNUW54AaABAg] 1. By using a simple Implicit Differentiation method, we can get that y’ = -x/y. 2. Or we can use polar coordinate system, set x = r cos theta, y = r sin theta, so y’(x) = y’(theta)/x’(theta) = x/(-y) as well.



@TedsEscapades 　오래 전

Still easier to differentiate,  but always nice to see graphical solution.

2026-08-18 16:26

[ytcid:UgzPU6R3HIrMgkV4KlF4AaABAg] Still easier to differentiate, but always nice to see graphical solution.



@cosmolbfu67 　오래 전

2x+2y.y'=0
y'=-2x/2y=-x/y
y'(3,-4)= -3/-4 =3/4

2026-08-19 00:28

[ytcid:UgwgOg4StVlUNLNPfsJ4AaABAg] 2x+2y.y'=0 y'=-2x/2y=-x/y y'(3,-4)= -3/-4 =3/4



@AOOA926 　오래 전

Just use implicit differentiation for a longer way

2026-08-18 23:35

[ytcid:Ugx2SSYQTlbc4OOfffF4AaABAg] Just use implicit differentiation for a longer way



@HowardThompson… 　오래 전

But implicit differentiation is so easy here. Honestly about as easy as this. dy/dx=-x/y and plug in (3,-4)

2026-08-18 21:38

[ytcid:UgykxYdhoKtknfeTKzl4AaABAg] But implicit differentiation is so easy here. Honestly about as easy as this. dy/dx=-x/y and plug in (3,-4)



@russelltaylor7… 　오래 전

2x+2yy'=0
2yy'=-2x
y'=-x/y

y(1)-x(-x/y)///y²

y+x²/y//y² =-25/y³
y"=-25/y³

2026-08-20 07:29

[ytcid:Ugwpfh756YBpclfrOcl4AaABAg] 2x+2yy'=0 2yy'=-2x y'=-x/y y(1)-x(-x/y)///y² y+x²/y//y² =-25/y³ y"=-25/y³



@surenazand 　오래 전

If you can, please show from ellipse equation,if P(x,y) is a point of ellipse.Then the distance between P and focus is equal to eccentricity times its distance from directrix.

2026-08-19 23:54

[ytcid:UgzAdVLfenWU2LQKrEt4AaABAg] If you can, please show from ellipse equation,if P(x,y) is a point of ellipse.Then the distance between P and focus is equal to eccentricity times its distance from directrix.