Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1367

Question Number 75983 Answers: 0 Comments: 2

show that cos^6 x+sin^6 x=(1/8)(5+3cos4x)

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{cos}^{\mathrm{6}} \mathrm{x}+\mathrm{sin}^{\mathrm{6}} \mathrm{x}=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{5}+\mathrm{3cos4x}\right) \\ $$

Question Number 75976 Answers: 0 Comments: 3

hello solve it in ]−π;π] and place solutions in trigonometric circle. cos^6 x+sin^6 x=(3/8)((√3)sin4x+(8/3)) please help me...

$$\left.\mathrm{h}\left.\mathrm{ello}\:\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\right]−\pi;\pi\right]\:\mathrm{and}\:\mathrm{place}\:\mathrm{solutions} \\ $$$$\mathrm{in}\:\mathrm{trigonometric}\:\mathrm{circle}. \\ $$$$\mathrm{cos}^{\mathrm{6}} \mathrm{x}+\mathrm{sin}^{\mathrm{6}} \mathrm{x}=\frac{\mathrm{3}}{\mathrm{8}}\left(\sqrt{\mathrm{3}}\mathrm{sin4x}+\frac{\mathrm{8}}{\mathrm{3}}\right) \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}... \\ $$

Question Number 76077 Answers: 2 Comments: 3

Find the maximum area of an isosceles triangle inscribed in an ellipse (x^2 /a^2 ) + (y^2 /b^2 ) = 1with its vetrex at one end of the major axis ? ?

$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{isosceles}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{ellipse}}\:\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{{a}}^{\mathrm{2}} }\:+\:\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} }\:=\:\mathrm{1}\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{vetrex}}\: \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{end}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\:?\:? \\ $$

Question Number 75960 Answers: 1 Comments: 2

prove that ∫_0 ^(π/2) ln(sinx)dx=−(π/2)ln2

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sinx}\right){dx}=−\frac{\pi}{\mathrm{2}}{ln}\mathrm{2} \\ $$

Question Number 75955 Answers: 2 Comments: 0

help me

$${help}\:{me}\: \\ $$$$ \\ $$

Question Number 75954 Answers: 0 Comments: 2

prove that (ann(I),+,.) identical in (R,+,.)?

$${prove}\:{that}\:\left({ann}\left({I}\right),+,.\right)\:{identical}\:{in}\:\left({R},+,.\right)? \\ $$

Question Number 75953 Answers: 0 Comments: 0

prove that (C(I),+,.) identical in (R,+,.)?

$${prove}\:{that}\:\left({C}\left({I}\right),+,.\right)\:{identical}\:{in}\:\left({R},+,.\right)? \\ $$

Question Number 75952 Answers: 0 Comments: 1

are this (cent(R),+,.)identical in the ring (R,+,.) ? pleas sir are you can help me?

$${are}\:{this}\:\left({cent}\left({R}\right),+,.\right){identical}\:{in}\:{the}\:{ring}\:\left({R},+,.\right)\:? \\ $$$${pleas}\:{sir}\:{are}\:{you}\:{can}\:{help}\:{me}? \\ $$

Question Number 75951 Answers: 0 Comments: 0

give ∫_0 ^(π/2) (x^2 /(1−cosx))dx at form of serie.

$${give}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}−{cosx}}{dx}\:\:{at}\:{form}\:{of} \\ $$$${serie}. \\ $$

Question Number 75950 Answers: 0 Comments: 2

give ∫_0 ^(π/2) (x/(sinx))dx at form of serie.

$${give}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{sinx}}{dx}\:\:{at}\:{form}\:{of}\:{serie}. \\ $$

Question Number 75940 Answers: 0 Comments: 0

Given that a∈Z and k∈Z and [a+x] = a +[x] = k a) show that k−a≤ x≤ k−a +1 b) Deduce from (a)) that [x+a] = [x] +a

$${Given}\:{that}\:{a}\in\mathbb{Z}\:{and}\:{k}\in\mathbb{Z}\:{and}\:\left[{a}+{x}\right]\:=\:{a}\:+\left[{x}\right]\:=\:{k} \\ $$$$\left.{a}\right)\:{show}\:{that}\:\:{k}−{a}\leqslant\:{x}\leqslant\:{k}−{a}\:+\mathrm{1} \\ $$$$\left.{b}\left.\right)\:{Deduce}\:{from}\:\left({a}\right)\right)\:{that}\:\left[{x}+{a}\right]\:=\:\left[{x}\right]\:+{a} \\ $$

Question Number 75939 Answers: 0 Comments: 2

Question Number 75938 Answers: 0 Comments: 2

solve the inequality ln(x^2 −4e^2 )< 1 + ln3x

$${solve}\:{the}\:{inequality} \\ $$$$\:{ln}\left({x}^{\mathrm{2}} −\mathrm{4}{e}^{\mathrm{2}} \right)<\:\mathrm{1}\:+\:{ln}\mathrm{3}{x} \\ $$

Question Number 75937 Answers: 1 Comments: 0

find the set of values of x for which ((ln x + 2)/(lnx−2)) > ((1−lnx)/(1+lnx))

$${find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{for}\:{which}\: \\ $$$$\:\:\frac{{ln}\:{x}\:+\:\mathrm{2}}{{lnx}−\mathrm{2}}\:>\:\frac{\mathrm{1}−{lnx}}{\mathrm{1}+{lnx}} \\ $$

Question Number 75936 Answers: 0 Comments: 2

prove that if [((x + 1)/x)] = 0 then x ≤ −1

$${prove}\:{that}\:{if}\:\left[\frac{{x}\:+\:\mathrm{1}}{{x}}\right]\:=\:\mathrm{0}\:{then}\:{x}\:\leqslant\:−\mathrm{1} \\ $$

Question Number 75934 Answers: 0 Comments: 0

how do i sketch the curve y = x−[x] ,for 0≤x<6

$${how}\:{do}\:{i}\:{sketch}\:{the}\:{curve}\: \\ $$$${y}\:=\:{x}−\left[{x}\right]\:,{for}\:\mathrm{0}\leqslant{x}<\mathrm{6} \\ $$

Question Number 75933 Answers: 0 Comments: 2

solve the inequality a. ln(2x−e) >1 b. (lnx)^2 −lnx−6<0 c. ∣x∣ + ∣x+2∣ ≥ 2 d. ∣2x−5∣ + ∣x +2∣ > 7

$${solve}\:{the}\:{inequality} \\ $$$${a}.\:\:{ln}\left(\mathrm{2}{x}−{e}\right)\:>\mathrm{1} \\ $$$${b}.\:\left({lnx}\right)^{\mathrm{2}} −{lnx}−\mathrm{6}<\mathrm{0} \\ $$$${c}.\:\mid{x}\mid\:+\:\mid{x}+\mathrm{2}\mid\:\geqslant\:\mathrm{2} \\ $$$${d}.\:\mid\mathrm{2}{x}−\mathrm{5}\mid\:+\:\mid{x}\:+\mathrm{2}\mid\:>\:\mathrm{7} \\ $$

Question Number 75932 Answers: 1 Comments: 1

solve for x the following a. ∣x∣ + 3x −4 =0 b. ∣x∣−1 = 0 c. x^2 +3∣x∣ +2 =0

$${solve}\:{for}\:{x}\:{the}\:{following} \\ $$$${a}.\:\mid{x}\mid\:+\:\mathrm{3}{x}\:−\mathrm{4}\:=\mathrm{0} \\ $$$${b}.\:\:\mid{x}\mid−\mathrm{1}\:=\:\mathrm{0} \\ $$$${c}.\:{x}^{\mathrm{2}} +\mathrm{3}\mid{x}\mid\:+\mathrm{2}\:=\mathrm{0} \\ $$$$ \\ $$

Question Number 75931 Answers: 0 Comments: 4

Evaluate a. lim_(x→∞) (((x^2 +3)/(27x^2 −1)))^(1/3) b. lim_(x→−∞) ((x−2)/(√(x^2 +1))) c. lim_(x→∞) ((x^2 +2)/(2x−3)) d. lim_(x→∞) 2x + 1 − (√(4x^2 +5))

$${Evaluate} \\ $$$${a}.\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\frac{{x}^{\mathrm{2}} +\mathrm{3}}{\mathrm{27}{x}^{\mathrm{2}} −\mathrm{1}}} \\ $$$${b}.\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{{x}−\mathrm{2}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${c}.\underset{{x}\rightarrow\infty} {\:\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}−\mathrm{3}} \\ $$$${d}.\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{2}{x}\:+\:\mathrm{1}\:−\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{5}} \\ $$

Question Number 75930 Answers: 0 Comments: 0

consider the function f(x) = { ((1+2x^2 , if x is rational)),((1 + x^4 , if x is irrational)) :} Use the sandwich(pinchin) theorem to prove that lim_(x→0) f(x) = 1.

$${consider}\:{the}\:{function} \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} ,\:{if}\:{x}\:{is}\:{rational}}\\{\mathrm{1}\:+\:{x}^{\mathrm{4}} ,\:{if}\:{x}\:{is}\:{irrational}}\end{cases} \\ $$$${Use}\:{the}\:{sandwich}\left({pinchin}\right)\:{theorem}\:{to} \\ $$$${prove}\:{that}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{1}. \\ $$

Question Number 75929 Answers: 0 Comments: 2

Evaluate lim_(x→−∞) [(√(1−xe^x )) ]

$${Evaluate} \\ $$$$\underset{{x}\rightarrow−\infty} {\:\mathrm{lim}}\:\left[\sqrt{\mathrm{1}−{xe}^{{x}} }\:\right] \\ $$

Question Number 75925 Answers: 0 Comments: 0

Let OA^(→) = i+3j−2k and OB^(→) =3i+j−2k. The vector OC^(→) bisecting the ∠AOB and C being a point on the line AB is

$$\mathrm{Let}\:\overset{\rightarrow} {{OA}}=\:\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}−\mathrm{2}\boldsymbol{\mathrm{k}}\:\mathrm{and}\:\overset{\rightarrow} {{OB}}=\mathrm{3}\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}−\mathrm{2}\boldsymbol{\mathrm{k}}. \\ $$$$\mathrm{The}\:\mathrm{vector}\:\overset{\rightarrow} {{OC}}\:\mathrm{bisecting}\:\mathrm{the}\:\angle{AOB}\:\mathrm{and} \\ $$$${C}\:\:\mathrm{being}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{line}\:{AB}\:\mathrm{is} \\ $$

Question Number 75924 Answers: 0 Comments: 3

Thr value of ∫_(0 ) ^(π/2) cosec (x−(π/3))cosec (x−(π/6))dx is

$$\mathrm{Thr}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\underset{\mathrm{0}\:} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{cosec}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)\mathrm{cosec}\:\left({x}−\frac{\pi}{\mathrm{6}}\right){dx}\:\:\mathrm{is} \\ $$

Question Number 75921 Answers: 0 Comments: 1

Question Number 75916 Answers: 0 Comments: 1

x^3 +x^2 −24x+36=0 prove that x=2,3,−6.

$${x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{24}{x}+\mathrm{36}=\mathrm{0} \\ $$$${prove}\:{that}\:{x}=\mathrm{2},\mathrm{3},−\mathrm{6}. \\ $$

Question Number 75913 Answers: 0 Comments: 1

x^3 −7x+6=0 prove that x=2,−3,1 .

$${x}^{\mathrm{3}} −\mathrm{7}{x}+\mathrm{6}=\mathrm{0} \\ $$$${prove}\:{that}\:{x}=\mathrm{2},−\mathrm{3},\mathrm{1}\:. \\ $$

Pg 1362 Pg 1363 Pg 1364 Pg 1365 Pg 1366 Pg 1367 Pg 1368 Pg 1369 Pg 1370 Pg 1371

Terms of Service

Contact: info@tinkutara.com