Question

Find the set of values of $a\in\mathbb{R}$ such that $f(x)=ax^2+x$ and $g(x)=\ln(1+x)$ have a common tangent in a common point.

score 49 · Answer 1 · 2020-03-07 16:42:57

49

Views

Find the set of values of $a\in\mathbb{R}$ such that $f(x)=ax^2+x$ and $g(x)=\ln(1+x)$ have a common tangent in a common point.

Published on 07 Mar 2020 - 16:42

score 52 · Answer 2 · 2020-03-11 13:18:47

52

Views

prove that sum of perimeters of APQ,BRS,CTV is equal to perimeter of ABC

Published on 11 Mar 2020 - 13:18

score 366 · Answer 3 · 2020-03-12 08:35:52

366

Views

Equation of tangent with homogeneous coordinates

Published on 12 Mar 2020 - 8:35

score 75 · Answer 4 · 2020-03-13 17:42:14

75

Views

Assuming that " slope of the tangent at $x=a$ " and " $f'(a)$" are not identical by definition , how can their identity be shown algebraically?

Published on 13 Mar 2020 - 17:42

score 60 · Answer 5 · 2020-03-14 06:59:56

60

Views

Find center of circle, which tangent to $y=2$ at $(3,2)$ and $y=-x\sqrt 3 +2$

Published on 14 Mar 2020 - 6:59

score 71 · Answer 6 · 2020-03-14 14:14:23

71

Views

Find an equation of a line tangent to $y=x^4-6x$ and perpendicular to the line $x-2y+6 = 0$. How to solve?

Published on 14 Mar 2020 - 14:14

score 126 · Answer 7 · 2026-02-23 12:56:58

126

Views

Prove that there exists a line passing through M$(\alpha,\beta)$ which is tangent to the graph of $f$.

Published on 23 Feb 2026 - 12:56

score 110 · Answer 8 · 2020-03-16 21:37:13

110

Views

How to calculate the tangent line of $\ln(x)$ through $(2,6)$ by hand?

Published on 16 Mar 2020 - 21:37

score 486 · Answer 9 · 2020-03-17 02:30:37

486

Views

Function with two conditions

Published on 17 Mar 2020 - 2:30

score 184 · Answer 10 · 2020-03-22 09:20:11

184

Views

incircle tanget to triangle at D and incirles of ADC ADB

Published on 22 Mar 2020 - 9:20

score 90 · Answer 11 · 2020-03-22 19:01:50

90

Views

Find Equation of a tangent of a Trig graph given domain of x and angle

Published on 22 Mar 2020 - 19:01

score 58 · Answer 12 · 2020-03-22 19:37:54

58

Views

How do I determine the x-coordinates of the points of intersection of a tangent line and the parabola y = x^2?

Published on 22 Mar 2020 - 19:37

score 350 · Answer 13 · 2020-03-23 09:36:04

350

Views

if four circles touch each other externally then points of contact are concyclic

Published on 23 Mar 2020 - 9:36

score 2k · Answer 14 · 2020-03-27 18:27:00

2k

Views

Consider the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$. Find the equations of common tangents to the two circles.

Published on 27 Mar 2020 - 18:27

score 949 · Answer 15 · 2020-04-04 13:46:23

949

Views

A curve has the parametric equations $x=2t^2$ and $y=4t$. What is the value(s) of $k$ such that $y=x+k$ is a tangent to the curve?

Published on 04 Apr 2020 - 13:46

List Question

Find the set of values of $a\in\mathbb{R}$ such that $f(x)=ax^2+x$ and $g(x)=\ln(1+x)$ have a common tangent in a common point.

prove that sum of perimeters of APQ,BRS,CTV is equal to perimeter of ABC

Equation of tangent with homogeneous coordinates

Assuming that " slope of the tangent at $x=a$ " and " $f'(a)$" are not identical by definition , how can their identity be shown algebraically?

Find center of circle, which tangent to $y=2$ at $(3,2)$ and $y=-x\sqrt 3 +2$

Find an equation of a line tangent to $y=x^4-6x$ and perpendicular to the line $x-2y+6 = 0$. How to solve?

Prove that there exists a line passing through M$(\alpha,\beta)$ which is tangent to the graph of $f$.

How to calculate the tangent line of $\ln(x)$ through $(2,6)$ by hand?

Function with two conditions

incircle tanget to triangle at D and incirles of ADC ADB

Find Equation of a tangent of a Trig graph given domain of x and angle

How do I determine the x-coordinates of the points of intersection of a tangent line and the parabola y = x^2?

if four circles touch each other externally then points of contact are concyclic

Consider the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$. Find the equations of common tangents to the two circles.

A curve has the parametric equations $x=2t^2$ and $y=4t$. What is the value(s) of $k$ such that $y=x+k$ is a tangent to the curve?

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