Все публикации

0:11:36

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) ?

0:03:59

Determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙+𝟏).

0:02:58

Determine all the asymptotes of the curve 𝒚=(𝒙+𝟑)/(𝒙+𝟐).

0:02:49

Determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑).

0:06:20

Determine all the asymptotes of the curve 𝒚=√𝒙+𝟒/√(𝒙+𝟒).

0:15:12

Determine all the asymptotes of the curve y=(1-x^2)/(x^2+1).

0:16:53

Determine all the asymptotes of the curve y=(x^2+4)/(x-3).

0:18:47

Determine all the asymptotes of the curve y=(x^2+x-6)/(x^2+2x-8).

1:03:24

Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)

0:28:27

Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)

0:33:00

Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)

0:24:32

Asymptotes of a curve given in polar form

0:29:16

Asymptotes of a curve given in parametric form

0:42:10

Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)

0:22:20

Definition of Asymptotes of Curves and its types

0:08:21

f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.

0:12:25

If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.

0:06:49

f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)

0:12:36

f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)

0:10:56

cos⁡x strictly less than (sin⁡x/x)^3 for all x∈(0, π/2)

0:22:27

Definition of random variable and its examples

0:07:17

1-x strictly less than e^(-x) strictly less than 1-x+x^2/2 for all positive numbers x

0:05:22

tan⁡x/x strictly greater than x/sin⁡x or cos⁡x strictly less than (sin⁡x/x)^2 for x∈(0, π/2)

0:06:37

(sin⁡α-sin⁡β)/(cos⁡β-cos⁡α )=cot⁡θ for some θ∈(α,β)⊂[α,β]⊂(0,π/2)