Question and Answers Forum

AllQuestion and Answers: Page 267

Question Number 194373 Answers: 0 Comments: 0

Show Σ_(i=1) ^n ((1/(2i−1))− (1/(2i)))=Σ_(i=1) ^n (1/(n+i))

$${Show}\:\:\: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{i}−\mathrm{1}}−\:\frac{\mathrm{1}}{\mathrm{2}{i}}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}+{i}}\: \\ $$$$ \\ $$

Question Number 194363 Answers: 1 Comments: 1

Question Number 194359 Answers: 1 Comments: 1

v2.282 has been published. This update fixes issues with missed notifications and adds an arbitarary precision scientific calculator.

$${v}\mathrm{2}.\mathrm{282}\:\mathrm{has}\:\mathrm{been}\:\mathrm{published}.\:\mathrm{This} \\ $$$$\mathrm{update}\:\mathrm{fixes}\:\mathrm{issues}\:\mathrm{with}\:\mathrm{missed} \\ $$$$\mathrm{notifications}\:\mathrm{and}\:\mathrm{adds}\:\mathrm{an} \\ $$$$\mathrm{arbitarary}\:\mathrm{precision}\: \\ $$$$\mathrm{scientific}\:\mathrm{calculator}. \\ $$

Question Number 194352 Answers: 0 Comments: 0

(dy/dx) = ((x^2 +y^2 )/( (√(x+y))))

$$\:\:\: \frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\:\sqrt{\mathrm{x}+\mathrm{y}}} \\ $$

Question Number 194350 Answers: 2 Comments: 0

Question Number 194344 Answers: 2 Comments: 0

Question Number 194343 Answers: 3 Comments: 0

⌊9.9^− ⌋ = ?

$$\lfloor\mathrm{9}.\overset{−} {\mathrm{9}}\rfloor\:=\:? \\ $$

Question Number 194338 Answers: 2 Comments: 0

Question Number 194335 Answers: 1 Comments: 0

Question Number 194334 Answers: 0 Comments: 2

lim_(x→0^+ ) (((√((1/x)+(√(x/(ln x)))))−(√((1/x)−(√((ln x)/x)))))/(ln 3x))

$$\:\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\frac{\mathrm{1}}{\mathrm{x}}+\sqrt{\frac{\mathrm{x}}{\mathrm{ln}\:\mathrm{x}}}}−\sqrt{\frac{\mathrm{1}}{\mathrm{x}}−\sqrt{\frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}}}}}{\mathrm{ln}\:\mathrm{3x}}\:\:\: \\ $$

Question Number 194331 Answers: 1 Comments: 0

Question Number 194327 Answers: 1 Comments: 0

If ta4θ = 1, find the values of θ.

$$\mathrm{If}\:\mathrm{ta4}\theta\:=\:\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta. \\ $$

Question Number 194326 Answers: 1 Comments: 0

(√(((√(x^2 +66^2 +x))/x) )) −(√(x(√(x^2 +66^2 ))−x^2 )) = 5

$$\:\:\sqrt{\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} +\mathrm{x}}}{\mathrm{x}}\:}\:−\sqrt{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{5}\: \\ $$

Question Number 194325 Answers: 1 Comments: 0

value of f(x,y,z)= x^4 +y^4 +z^4 subject to x^2 +y^2 +z^2 =5

$$\: \: \: \: \\ $$$$ \mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\:\mathrm{x}^{\mathrm{4}} +\mathrm{y}^{\mathrm{4}} +\mathrm{z}^{\mathrm{4}} \: \\ $$$$\:\mathrm{subject}\:\mathrm{to}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{5}\: \\ $$

Question Number 194322 Answers: 0 Comments: 0

Question Number 194321 Answers: 1 Comments: 0

find min −(((x−y)(((xy)/4)−4)^2 )/(xy)) s. t. x>0>y

$$\mathrm{find}\:\mathrm{min}\:\:−\frac{\left({x}−{y}\right)\left(\frac{{xy}}{\mathrm{4}}−\mathrm{4}\right)^{\mathrm{2}} }{{xy}} \\ $$$$\mathrm{s}.\:\mathrm{t}.\:\:{x}>\mathrm{0}>{y} \\ $$

Question Number 194317 Answers: 0 Comments: 0

Question Number 194316 Answers: 0 Comments: 1

if x∈R & x^x^6 =((√2))^(√2) ⇒ x=?

$${if}\:\:{x}\in{R}\:\:\&\:\:{x}^{{x}^{\mathrm{6}} } =\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \:\Rightarrow\:\:{x}=? \\ $$

Question Number 194315 Answers: 1 Comments: 0

4sin 2x cos x +1 = 2cos 4x

$$\:\:\:\: \\ $$$$ \mathrm{4sin}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{x}\:+\mathrm{1}\:=\:\mathrm{2cos}\:\mathrm{4x}\: \\ $$$$\: \\ $$

Question Number 194312 Answers: 0 Comments: 0

Question Number 194304 Answers: 1 Comments: 0

Question Number 194301 Answers: 1 Comments: 0

Resolution de l exercice du 28.6.23 (envoye par universe ) Q194116

$$\boldsymbol{\mathrm{Resolution}}\:\boldsymbol{\mathrm{de}}\:\boldsymbol{\mathrm{l}}\:\boldsymbol{\mathrm{exercice}}\:\boldsymbol{\mathrm{du}}\:\mathrm{28}.\mathrm{6}.\mathrm{23} \\ $$$$\:\:\left({env}\mathrm{o}{ye}\:{par}\:{universe}\:\right) \\ $$$$\boldsymbol{{Q}}\mathrm{194116} \\ $$$$ \\ $$

Question Number 194297 Answers: 1 Comments: 0

Let a , b , c be real positive numbers & abc=1 prove that ((ab)/(a^5 +b^5 +ab))+((bc)/(b^5 +c^5 +bc))+((ac)/(a^5 +c^5 +ac))≤1

$${Let}\:{a}\:,\:{b}\:,\:{c}\:{be}\:\:{real}\:{positive}\:{numbers}\:\&\: \\ $$$${abc}=\mathrm{1}\: \\ $$$${prove}\:{that} \\ $$$$\frac{{ab}}{{a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{ab}}+\frac{{bc}}{{b}^{\mathrm{5}} +{c}^{\mathrm{5}} +{bc}}+\frac{{ac}}{{a}^{\mathrm{5}} +{c}^{\mathrm{5}} +{ac}}\leqslant\mathrm{1} \\ $$

Question Number 194295 Answers: 1 Comments: 0

Question Number 194292 Answers: 0 Comments: 0

Question Number 194286 Answers: 2 Comments: 0

find lim_(x→0) ⌊ ((tan(x))/x)⌋

$$ \\ $$$$\:\:\boldsymbol{{find}}\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\lfloor\:\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{x}}}\rfloor \\ $$

Pg 262 Pg 263 Pg 264 Pg 265 Pg 266 Pg 267 Pg 268 Pg 269 Pg 270 Pg 271

Contact: info@tinkutara.com