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AllQuestion and Answers: Page 508

Question Number 168229 Answers: 1 Comments: 0

Question Number 168225 Answers: 2 Comments: 0

hi ! x ∈ ](π/4) ; (π/3)[ f (x) = (1/(cos x)) primitive of f(x).

$$\mathrm{hi}\:! \\ $$$$\left.{x}\:\in\:\right]\frac{\pi}{\mathrm{4}}\:;\:\frac{\pi}{\mathrm{3}}\left[\right. \\ $$$${f}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{{cos}\:{x}} \\ $$$$\mathrm{primitive}\:\mathrm{of}\:{f}\left({x}\right). \\ $$

Question Number 168210 Answers: 1 Comments: 0

Question Number 168209 Answers: 0 Comments: 0

Question Number 168208 Answers: 2 Comments: 1

If (x+yi)^4 =a+bi, show that a^2 +b^2 =(x^2 +y^2 )^4

$$\:{If}\:\left({x}+{y}\boldsymbol{{i}}\right)^{\mathrm{4}} ={a}+{b}\boldsymbol{{i}}, \\ $$$$\:{show}\:{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{4}} \\ $$

Question Number 168206 Answers: 1 Comments: 0

Question Number 168203 Answers: 1 Comments: 0

Question Number 168198 Answers: 0 Comments: 0

Question Number 168190 Answers: 0 Comments: 5

Question Number 168189 Answers: 1 Comments: 11

Question Number 168188 Answers: 4 Comments: 1

∫ ((1−sin 2x)/((1+sin 2x)^2 )) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$

Question Number 168187 Answers: 2 Comments: 0

Prove that : sinh^(−1) tanθ = log tan((θ/2)+(π/4)) Mastermind

$${Prove}\:{that}\::\: \\ $$$${sinh}^{−\mathrm{1}} {tan}\theta\:=\:{log}\:{tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168185 Answers: 0 Comments: 0

Separate cos^(−1) e^(iθ) into real and imaginary parts. Mastermind

$${Separate}\:{cos}^{−\mathrm{1}} {e}^{{i}\theta} \:{into}\: \\ $$$${real}\:{and}\:{imaginary}\:{parts}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168180 Answers: 1 Comments: 0

Question Number 168178 Answers: 0 Comments: 0

Question Number 168179 Answers: 1 Comments: 0

Question Number 168176 Answers: 1 Comments: 0

If , f(x)=(( ∣ sin(2x)∣)/(∣sin(x)∣+∣cos(x)∣ +1)) then : R_( f) =? ( range )

$$ \\ $$$$\:\:\: \\ $$$$\:\:\:\mathrm{I}{f}\:,\:\:{f}\left({x}\right)=\frac{\:\:\mid\:{sin}\left(\mathrm{2}{x}\right)\mid}{\mid{sin}\left({x}\right)\mid+\mid{cos}\left({x}\right)\mid\:+\mathrm{1}} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:\::\:\:\:\:\:\:{R}_{\:{f}} \:=?\:\:\:\:\:\:\:\:\left(\:{range}\:\right)\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 168164 Answers: 0 Comments: 1

Find the total energy (in Joules) of a particle of mass 4.0×10^(−11) kg moving at 80% the speed of light.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{energy}\:\left({in}\:{Joules}\right) \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{4}.\mathrm{0}×\mathrm{10}^{−\mathrm{11}} \mathrm{kg} \\ $$$$\mathrm{moving}\:\mathrm{at}\:\mathrm{80\%}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{light}. \\ $$

Question Number 168161 Answers: 1 Comments: 1

Question Number 168159 Answers: 0 Comments: 0

Question Number 168158 Answers: 0 Comments: 0

Question Number 168157 Answers: 0 Comments: 0

Question Number 168147 Answers: 0 Comments: 0

calculate :: lim_(x→0) (((tan (1+tan x))/(tan (1+sin x))))^(1/x^3 ) =?

$$\mathrm{calculate}\:\:::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt[{\mathrm{x}^{\mathrm{3}} }]{\frac{\mathrm{tan}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}}=? \\ $$

Question Number 168144 Answers: 1 Comments: 0

lim_(x→0) ((x^3 (√(1+x)) −sin^3 x −(1/2)x^3 tan x)/((((1+2x^3 ))^(1/3) −1)ln (1+x^2 )))=?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} \sqrt{\mathrm{1}+{x}}\:−\mathrm{sin}\:^{\mathrm{3}} {x}\:−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}{\left(\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{2}{x}^{\mathrm{3}} }−\mathrm{1}\right)\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}=?\:\:\:\:\:\:\:\: \\ $$

Question Number 168143 Answers: 2 Comments: 0

lim_(x→0) ((1−cos (1−cos x))/x^4 ) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{{x}^{\mathrm{4}} }\:=?\:\:\:\:\:\: \\ $$

Question Number 168138 Answers: 2 Comments: 0

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