Question

proving that $\lim_{x \to \pi} \frac{1+\cos x }{1+\cos 3x}=\frac{1}{9}$ without L'Hôpital.

score 115 · Answer 1 · 2026-03-25 01:18:35

115

Views

proving that $\lim_{x \to \pi} \frac{1+\cos x }{1+\cos 3x}=\frac{1}{9}$ without L'Hôpital.

Published on 25 Mar 2026 - 1:18

score 484 · Answer 2 · 2026-04-11 21:53:16

484

Views

Closed algebraic form of $\cos(\frac{\pi}{7})$

Published on 11 Apr 2026 - 21:53

score 173 · Answer 3 · 2026-04-10 21:55:20

173

Views

$3- \log_3(p) = \log_p(9)$, $p = ?$

Published on 10 Apr 2026 - 21:55

score 67 · Answer 4 · 2026-03-25 01:12:04

67

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Find an equation for the largest sphere that is centered at $(2,1,-2)$ and intersects the sphere $x^2 +y^2+z^2=1$

Published on 25 Mar 2026 - 1:12

score 121 · Answer 5 · 2026-03-31 05:02:33

121

Views

Justify each step with a property, definition or an operation

Published on 31 Mar 2026 - 5:02

score 57 · Answer 6 · 2018-02-11 11:46:37

57

Views

Solve the equation $\sqrt{x^2-(a+b)x+ab}+\sqrt{x^2-(b+c)x+bc}=0$ where $a$, $b$, and $c$ are real numbers

Published on 11 Feb 2018 - 11:46

score 873 · Answer 7 · 2026-03-25 11:27:15

873

Views

If the equation $x^2+qx+rp=0$ and $x^2+rx+pq=0$ have a common root, the other root will satisfy which of the equations

Published on 25 Mar 2026 - 11:27

score 906 · Answer 8 · 2026-03-25 11:27:14

If $a,b$ are the roots of $x^2-px+q=0$ and $a',b'$ are the roots of $x^2-p'x+q'=0$, then find the value of $(a-a')^2+(b-b')^2+(a-b')^2+(b-a)^2$

score 374 · Answer 9 · 2026-03-25 11:27:15

374

Views

If a is one of the root of the equation 4x^2+2x-1=0. Then find the other root

Published on 25 Mar 2026 - 11:27

score 89 · Answer 10 · 2026-03-25 10:55:58

89

Views

Finding the range of $\frac{x+1}{x^2+2}$

Published on 25 Mar 2026 - 10:55

score 637 · Answer 11 · 2026-04-11 16:14:16

637

Views

Find the missing numbers of a chart

Published on 11 Apr 2026 - 16:14

score 177 · Answer 12 · 2026-04-12 03:33:35

177

Views

Least degree of a polynomial given value of polynomial at $6$ points

Published on 12 Apr 2026 - 3:33

score 631 · Answer 13 · 2026-03-25 01:20:28

631

Views

Solving an Olympiad functional equation $f(f(n))=f(f(n+2)+2)=n$

Published on 25 Mar 2026 - 1:20

score 63 · Answer 14 · 2018-02-12 10:58:27

63

Views

find minimum of $A$ such that $\frac1x +\frac1y+\frac1z < 1$

Published on 12 Feb 2018 - 10:58

score 214 · Answer 15 · 2026-03-26 09:16:43

214

Views

Points on a line p equidistant from two planes

Published on 26 Mar 2026 - 9:16

List Question

proving that $\lim_{x \to \pi} \frac{1+\cos x }{1+\cos 3x}=\frac{1}{9}$ without L'Hôpital.

Closed algebraic form of $\cos(\frac{\pi}{7})$

$3- \log_3(p) = \log_p(9)$, $p = ?$

Find an equation for the largest sphere that is centered at $(2,1,-2)$ and intersects the sphere $x^2 +y^2+z^2=1$

Justify each step with a property, definition or an operation

Solve the equation $\sqrt{x^2-(a+b)x+ab}+\sqrt{x^2-(b+c)x+bc}=0$ where $a$, $b$, and $c$ are real numbers

If the equation $x^2+qx+rp=0$ and $x^2+rx+pq=0$ have a common root, the other root will satisfy which of the equations

If $a,b$ are the roots of $x^2-px+q=0$ and $a',b'$ are the roots of $x^2-p'x+q'=0$, then find the value of $(a-a')^2+(b-b')^2+(a-b')^2+(b-a)^2$

If a is one of the root of the equation 4x^2+2x-1=0. Then find the other root

Finding the range of $\frac{x+1}{x^2+2}$

Find the missing numbers of a chart

Least degree of a polynomial given value of polynomial at $6$ points

Solving an Olympiad functional equation $f(f(n))=f(f(n+2)+2)=n$

find minimum of $A$ such that $\frac1x +\frac1y+\frac1z < 1$

Points on a line p equidistant from two planes

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