Question and Answers Forum

AllQuestion and Answers: Page 1706

Question Number 37146 Answers: 0 Comments: 0

Question Number 37143 Answers: 0 Comments: 0

Why are following statements wrong? a) There exists a function with domain R satisfying f(x)<0 ∀x , f′(x)>0∀x and f′′(x)>0∀x. b) If f′′(c)=0 then (c,f(c)) is an inflection point.

$$\mathrm{Why}\:\mathrm{are}\:\mathrm{following}\:\mathrm{statements}\:\mathrm{wrong}? \\ $$$$\left.\mathrm{a}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{function}\:\mathrm{with}\:\mathrm{domain}\: \\ $$$$\mathrm{R}\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{x}\right)<\mathrm{0}\:\forall\mathrm{x}\:,\:\mathrm{f}'\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}\:\mathrm{and} \\ $$$$\mathrm{f}''\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}. \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{f}''\left(\mathrm{c}\right)=\mathrm{0}\:\mathrm{then}\:\left(\mathrm{c},\mathrm{f}\left(\mathrm{c}\right)\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{inflection} \\ $$$$\mathrm{point}. \\ $$

Question Number 37133 Answers: 0 Comments: 0

Question Number 37132 Answers: 0 Comments: 0

Question Number 37131 Answers: 0 Comments: 2

Question Number 37136 Answers: 0 Comments: 1

Question Number 37139 Answers: 2 Comments: 0

if α , β are the roots of the quadratic equation ax^2 +bx+c =0 then find the quadratic equation whose roots are α^(2 ) , β^2

$${if}\:\alpha\:,\:\beta\:\:{are}\:{the}\:{roots}\:{of}\:{the}\:{quadratic} \\ $$$${equation}\:{ax}^{\mathrm{2}} +{bx}+{c}\:=\mathrm{0}\:{then}\:\:{find} \\ $$$${the}\:{quadratic}\:{equation}\:{whose}\:{roots} \\ $$$${are}\:\:\alpha^{\mathrm{2}\:\:\:} ,\:\beta^{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$

Question Number 37137 Answers: 2 Comments: 4

Find minimum distance between y^2 =8x and x^2 +(y+6)^2 =1.

$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{y}^{\mathrm{2}} =\mathrm{8}{x}\:{and}\:{x}^{\mathrm{2}} +\left({y}+\mathrm{6}\right)^{\mathrm{2}} =\mathrm{1}. \\ $$

Question Number 37129 Answers: 0 Comments: 0

Question Number 37128 Answers: 0 Comments: 0

Question Number 37511 Answers: 0 Comments: 3

To the developer of Tinku Tara: dear sir: for some unknown reasons I don′t get any notification from the app when a post, in which I am involved, has been updated. Where is the problem and how can I solve it? Thank you!

$${To}\:{the}\:{developer}\:{of}\:{Tinku}\:{Tara}: \\ $$$${dear}\:{sir}:\:{for}\:{some}\:{unknown}\:{reasons} \\ $$$${I}\:{don}'{t}\:{get}\:{any}\:{notification}\:{from}\:{the} \\ $$$${app}\:{when}\:{a}\:{post},\:{in}\:{which}\:{I}\:{am}\:{involved}, \\ $$$${has}\:{been}\:{updated}.\:{Where}\:{is}\:{the} \\ $$$${problem}\:{and}\:{how}\:{can}\:{I}\:{solve}\:{it}? \\ $$$${Thank}\:{you}! \\ $$

Question Number 37123 Answers: 0 Comments: 1

draw ΔAB^ C and its image ΔA′B^′ C^′ after a reflection in line y=x if A(0,3),B(3,0),C(3,2).what is the line of symmetry of the two figures?

$${draw}\:\Delta{A}\overset{} {{B}C}\:{and}\:{its}\:{image}\:\:\Delta{A}'{B}^{'} {C}^{'} \: \\ $$$${after}\:{a}\:{reflection}\:{in}\:{line}\:{y}={x} \\ $$$${if}\:{A}\left(\mathrm{0},\mathrm{3}\right),{B}\left(\mathrm{3},\mathrm{0}\right),{C}\left(\mathrm{3},\mathrm{2}\right).{what}\:{is}\:{the} \\ $$$${line}\:{of}\:{symmetry}\:\:{of}\:{the}\:{two}\:{figures}? \\ $$

Question Number 37122 Answers: 0 Comments: 0

draw ΔAB^ C and its image ΔA′B^′ C^′ after a reflection in line y=x if A(0,3),B(3,0),C(3,2).what is the line of symmetry of the two figures?

Question Number 37110 Answers: 1 Comments: 2

prove that (cos𝛝−sin𝛝)^2 +(cosec𝛝+sin𝛝)^2 =2

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{cos}\vartheta}−\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{cosec}\vartheta}+\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} =\mathrm{2} \\ $$

Question Number 37108 Answers: 1 Comments: 0

If 4x+8cos x+tan x−2sec x−4log {cosx(1+sin x)}≥6 ∀ x ε [0,ψ) then largest value of ψ is ?

$$\mathrm{If}\:\mathrm{4}{x}+\mathrm{8cos}\:{x}+\mathrm{tan}\:{x}−\mathrm{2sec}\:{x}−\mathrm{4log}\:\left\{\mathrm{cos}{x}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\right\}\geqslant\mathrm{6} \\ $$$$\forall\:{x}\:\epsilon\:\left[\mathrm{0},\psi\right)\:\mathrm{then}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\psi\:\mathrm{is}\:? \\ $$