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Question Number 83205 Answers: 0 Comments: 2

∫_0 ^(ln2) (1/(cosh(x + ln4)))dx =

$$\int_{\mathrm{0}} ^{{ln}\mathrm{2}} \frac{\mathrm{1}}{{cosh}\left({x}\:+\:{ln}\mathrm{4}\right)}{dx}\:= \\ $$

Question Number 83202 Answers: 0 Comments: 4

find the first 4 terms in the maclaurin[ series expansion for ln (1 + 3x) hence show that if x^2 and higher powers of x are negleted, then (1 + 3x)^(3/x) = e^6 (1 −9x)

$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{4}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{maclaurin}\left[\right. \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{3}{x}\right)\:\mathrm{hence}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{if}\:{x}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{higher}\:\mathrm{powers}\:\mathrm{of}\:{x}\:\mathrm{are}\:\mathrm{negleted}, \\ $$$$\mathrm{then}\: \\ $$$$\:\:\:\left(\mathrm{1}\:+\:\mathrm{3}{x}\right)^{\frac{\mathrm{3}}{{x}}} \:=\:{e}^{\mathrm{6}} \left(\mathrm{1}\:−\mathrm{9}{x}\right) \\ $$

Question Number 82929 Answers: 2 Comments: 0

if 2B+A=45° show that; tan B= ((1−2tanA−tan^2 A)/(1+2tanA−tan^2 A))

$${if}\:\mathrm{2}{B}+{A}=\mathrm{45}° \\ $$$${show}\:{that}; \\ $$$${tan}\:{B}=\:\frac{\mathrm{1}−\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}}{\mathrm{1}+\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}} \\ $$

Question Number 82886 Answers: 0 Comments: 2

prove (tanx+cot^2 x)^2 =sex^2 x+cosec^2 x

$${prove}\: \\ $$$$\left({tanx}+{cot}^{\mathrm{2}} {x}\right)^{\mathrm{2}} ={sex}^{\mathrm{2}} {x}+{cosec}^{\mathrm{2}} {x} \\ $$

Question Number 82867 Answers: 0 Comments: 3

hello prove that ∫_0 ^(+∞) sin(x^4 )dx=sin((π/8))∫_0 ^(+∞) e^(−x^4 ) dx? verry nice day Good Bless You

$${hello}\:{prove}\:{that}\:\int_{\mathrm{0}} ^{+\infty} {sin}\left({x}^{\mathrm{4}} \right){dx}={sin}\left(\frac{\pi}{\mathrm{8}}\right)\int_{\mathrm{0}} ^{+\infty} {e}^{−{x}^{\mathrm{4}} } {dx}? \\ $$$${verry}\:{nice}\:{day}\:{Good}\:{Bless}\:{You} \\ $$

Question Number 82729 Answers: 1 Comments: 2

Question Number 82721 Answers: 1 Comments: 2

show that ∫xe^(−x^6 ) sin(x^3 ) dx=((Γ((5/6)))/3) 1F1[(5/6);(3/2);((−1)/4)]

$${show}\:{that}\: \\ $$$$\int{xe}^{−{x}^{\mathrm{6}} } \:{sin}\left({x}^{\mathrm{3}} \right)\:{dx}=\frac{\Gamma\left(\frac{\mathrm{5}}{\mathrm{6}}\right)}{\mathrm{3}}\:\mathrm{1}{F}\mathrm{1}\left[\frac{\mathrm{5}}{\mathrm{6}};\frac{\mathrm{3}}{\mathrm{2}};\frac{−\mathrm{1}}{\mathrm{4}}\right] \\ $$

Question Number 82639 Answers: 0 Comments: 3

Question Number 82616 Answers: 0 Comments: 0

Find the normalization constant ψ_((φ,θ)) =Ne^(iφ) sinθ

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{normalization}\:\mathrm{constant}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\psi_{\left(\phi,\theta\right)} =\mathrm{Ne}^{\mathrm{i}\phi} \mathrm{sin}\theta \\ $$

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Question Number 82497 Answers: 0 Comments: 0

Question Number 82415 Answers: 0 Comments: 1

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Question Number 82358 Answers: 0 Comments: 3

Show that: a_n = − rω^2 , show clearly how you arrive at your result.

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}} \:\:=\:\:−\:\mathrm{r}\omega^{\mathrm{2}} \:,\:\:\:\mathrm{show}\:\mathrm{clearly}\:\mathrm{how}\:\mathrm{you}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{your}\:\mathrm{result}. \\ $$

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Question Number 82176 Answers: 0 Comments: 3

Question Number 82138 Answers: 0 Comments: 1

Question Number 82110 Answers: 0 Comments: 0

Question Number 82084 Answers: 0 Comments: 2

Question Number 82034 Answers: 0 Comments: 1

Prove by maths induction tbat n^5 − n^3 is divisible by 24.

$$\boldsymbol{{P}}{rove}\:\:{by}\:\:{maths}\:\:{induction}\:\:{tbat} \\ $$$$\boldsymbol{{n}}^{\mathrm{5}} \:−\:\boldsymbol{{n}}^{\mathrm{3}} \:\:\boldsymbol{{is}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{24}. \\ $$

Question Number 81971 Answers: 1 Comments: 0

Question Number 81843 Answers: 2 Comments: 5

Question Number 81851 Answers: 0 Comments: 0

1)find ∫ (dx/((x+1)^3 (x^2 +1)^2 )) 2) calculate ∫_0 ^∞ (dx/((x+1)^3 (x^2 +1)^2 ))

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 81797 Answers: 0 Comments: 1

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