Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1388

Question Number 70163 Answers: 1 Comments: 0

Question Number 70162 Answers: 1 Comments: 0

Question Number 70161 Answers: 1 Comments: 0

Question Number 70159 Answers: 1 Comments: 1

Question Number 70150 Answers: 0 Comments: 1

prove that ∫_0 ^(π/2) (√((4−sin^2 x)))dx < ((π(√(14)))/4)

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\left(\mathrm{4}−{sin}^{\mathrm{2}} {x}\right)}{dx}\:<\:\frac{\pi\sqrt{\mathrm{14}}}{\mathrm{4}} \\ $$

Question Number 70147 Answers: 1 Comments: 4

Consider the functions f(x)=5×4^(−x) and g(x)=(0.25)^(2x) +4 For what values of x do these functions assume equal values?

$${Consider}\:{the}\:{functions}\: \\ $$$${f}\left({x}\right)=\mathrm{5}×\mathrm{4}^{−{x}} \:{and}\:{g}\left({x}\right)=\left(\mathrm{0}.\mathrm{25}\right)^{\mathrm{2}{x}} +\mathrm{4} \\ $$$${For}\:{what}\:{values}\:{of}\:{x}\:{do}\:{these}\: \\ $$$${functions}\:{assume}\:{equal}\:{values}? \\ $$

Question Number 70145 Answers: 1 Comments: 0

prove that ; arg(z1z2)=arg(z1)+arg(z2). arg(z1/z2)=arg(z1)−arg(z2).

$${prove}\:{that}\:;\:{arg}\left(\boldsymbol{{z}}\mathrm{1}\boldsymbol{{z}}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)+{arg}\left({z}\mathrm{2}\right). \\ $$$${arg}\left({z}\mathrm{1}/{z}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)−{arg}\left({z}\mathrm{2}\right). \\ $$

Question Number 70138 Answers: 1 Comments: 0

prove that e^(iθ) =e^(i(θ+2kΠ)) given that k=0,±1,±2...

$${prove}\:{that}\:\:\:{e}^{{i}\theta} ={e}^{{i}\left(\theta+\mathrm{2}{k}\Pi\right)} \:\:{given}\:{that}\:{k}=\mathrm{0},\pm\mathrm{1},\pm\mathrm{2}... \\ $$

Question Number 70135 Answers: 0 Comments: 1

sophie−Germain identity a^4 +4b^4 =((a+b)^2 +b^2 )((a−b)^2 +b^2 )

$${sophie}−{Germain}\:{identity} \\ $$$${a}^{\mathrm{4}} +\mathrm{4}{b}^{\mathrm{4}} =\left(\left({a}+{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left(\left({a}−{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$

Question Number 70132 Answers: 1 Comments: 1

Σ_(n=1) ^(3050) i^n

$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{3050}} {\sum}}\:{i}^{{n}} \\ $$

Question Number 70121 Answers: 1 Comments: 0

Question Number 70108 Answers: 1 Comments: 0

Question Number 70103 Answers: 2 Comments: 0

if m^3 +2p^3 =3mn, a^3 +b^3 =p^3 and a^2 +b^2 =n then prove that a+b=m.

$$\mathrm{if}\:\mathrm{m}^{\mathrm{3}} +\mathrm{2p}^{\mathrm{3}} =\mathrm{3mn},\:\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} =\mathrm{p}^{\mathrm{3}} \:\mathrm{and} \\ $$$$\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{n}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{a}+\mathrm{b}=\mathrm{m}. \\ $$

Question Number 70075 Answers: 0 Comments: 3

Question Number 70074 Answers: 1 Comments: 1

∫_1 ^2 [3+(1/t^2 )]dt=

$$\int_{\mathrm{1}} ^{\mathrm{2}} \left[\mathrm{3}+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right]{dt}= \\ $$

Question Number 70069 Answers: 1 Comments: 2

Π_(n=1) ^5 (((12n−2)^4 +18^2 )/((12n−8)^4 +18^2 )) =(((10^4 +324)(22^4 +324)(34^4 +324)(46^4 +324)(58^4 +324))/((4^4 +324)(16^4 +324)(28^4 +324)(40^4 +324)(52^4 +324)))

Question Number 70066 Answers: 2 Comments: 0

Solve a) e^(2x) −e^(x+1) −e^x +e<0 b)4.2^(2x) −9.2^x <−2 c)9^x −4.3^(x+1) +27>0

$${Solve} \\ $$$$\left.\mathrm{a}\right)\:{e}^{\mathrm{2}{x}} −{e}^{{x}+\mathrm{1}} −{e}^{{x}} +{e}<\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\mathrm{4}.\mathrm{2}^{\mathrm{2}{x}} −\mathrm{9}.\mathrm{2}^{{x}} <−\mathrm{2} \\ $$$$\left.{c}\right)\mathrm{9}^{{x}} −\mathrm{4}.\mathrm{3}^{{x}+\mathrm{1}} +\mathrm{27}>\mathrm{0} \\ $$$$ \\ $$

Question Number 70048 Answers: 1 Comments: 6

Question Number 70044 Answers: 0 Comments: 1

(√(2016 + 2007(√(2018 + 2009(√(2020 + 2011(√(2022 + …)))))))) = ...

$$\sqrt{\mathrm{2016}\:+\:\mathrm{2007}\sqrt{\mathrm{2018}\:+\:\mathrm{2009}\sqrt{\mathrm{2020}\:+\:\mathrm{2011}\sqrt{\mathrm{2022}\:+\:\ldots}}}}\:\:=\:\:... \\ $$

Question Number 70040 Answers: 1 Comments: 3

If, a^2 b^2 c^2 ((1/a^3 )+(1/b^3 )+(1/c^3 ))=a^3 +b^3 +c^3 than prove that a,b,c Successive Proportional.

$$\mathrm{If},\:\mathrm{a}^{\mathrm{2}} \mathrm{b}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{3}} }\right)=\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} \:\mathrm{than} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{Successive}\:\mathrm{Proportional}. \\ $$

Question Number 70035 Answers: 0 Comments: 4

Question Number 70031 Answers: 0 Comments: 0

∫[x]dx

$$\int\left[{x}\right]{dx} \\ $$

Question Number 70030 Answers: 1 Comments: 0

Find the convergence of Σ_(n=1) ^∞ (((1/n) + 1)/(−n^2 ))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\frac{\mathrm{1}}{{n}}\:+\:\mathrm{1}}{−{n}^{\mathrm{2}} } \\ $$

Question Number 70052 Answers: 1 Comments: 0

sin A+sin B=n and cos A+cos B=m sin (A+B)=?

$$ \\ $$$$\mathrm{sin}\:{A}+\mathrm{sin}\:{B}={n}\:\:\:\:\:\:\:\:\:{and}\:\:\:\:\:\:\:\:\mathrm{cos}\:{A}+\mathrm{cos}\:{B}={m} \\ $$$$\mathrm{sin}\:\left({A}+{B}\right)=? \\ $$

Question Number 70051 Answers: 2 Comments: 0

((a+b)/c)=((cos(((a−b)/2)))/(cos(c/2)))

$$\frac{{a}+{b}}{{c}}=\frac{{cos}\left(\frac{{a}−{b}}{\mathrm{2}}\right)}{{cos}\frac{{c}}{\mathrm{2}}} \\ $$

Question Number 70025 Answers: 0 Comments: 1

use ε-δ defintion to prove that lim_(x→0) (((√(1+x))−(√(1−x)))/x)=1

$${use}\:\varepsilon-\delta\:{defintion}\:{to}\:{prove}\:{that} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{x}}−\sqrt{\mathrm{1}−{x}}}{{x}}=\mathrm{1} \\ $$

Pg 1383 Pg 1384 Pg 1385 Pg 1386 Pg 1387 Pg 1388 Pg 1389 Pg 1390 Pg 1391 Pg 1392

Contact: info@tinkutara.com