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Question Number 32980 Answers: 1 Comments: 0

(d/dx)( determinant ((((x^2 +2)^(x^3 +3) ),2^x ,(cosx^x )),((log_2^(x+1) (x^2 +x^(2x) +3^ )),(xlnx),(sin^(−1) tanx)),(3,π^(sinhx) ,e^x )))=?

$$ \\ $$$$ \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\begin{vmatrix}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{x}^{\mathrm{3}} +\mathrm{3}} }&{\mathrm{2}^{\mathrm{x}} }&{\mathrm{cosx}^{\mathrm{x}} }\\{\mathrm{log}_{\mathrm{2}^{\mathrm{x}+\mathrm{1}} } \left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2x}} +\overset{} {\mathrm{3}}\right)}&{\mathrm{xlnx}}&{\mathrm{sin}^{−\mathrm{1}} \mathrm{tanx}}\\{\mathrm{3}}&{\pi^{\mathrm{sinhx}} }&{\mathrm{e}^{\mathrm{x}} }\end{vmatrix}\right)=? \\ $$$$ \\ $$

Question Number 33152 Answers: 0 Comments: 1

it is given that (1/n)Σ_(r=1) ^n x^r =2 and (√((1/n)Σ_(r=1) ^n (x_r )^2 −(1/n^2 )(Σ_(r=1) ^n )^2 ))= 3 determine in terms of n the value of. Σ_(r=1) ^n (x_r +1)^2

$${it}\:{is}\:{given}\:{that} \\ $$$$\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{x}^{{r}} =\mathrm{2}\:{and}\:\sqrt{\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\left({x}_{{r}} \right)^{\mathrm{2}} −\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left(\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\right)^{\mathrm{2}} }=\:\mathrm{3} \\ $$$${determine}\:{in}\:{terms}\:{of}\:{n}\:{the}\:{value} \\ $$$${of}. \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\left({x}_{{r}} +\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 32977 Answers: 1 Comments: 0

Prove that ^n C_r +^n C_(r+1) =^(n+1) C_(r+1)

$${Prove}\:{that}\:\:^{{n}} {C}_{{r}} \:\:+\:^{{n}} {C}_{{r}+\mathrm{1}} \:=\:^{{n}+\mathrm{1}} {C}_{{r}+\mathrm{1}} \\ $$$$ \\ $$

Question Number 33125 Answers: 0 Comments: 0

let give u_n = ∫_0 ^π ((cos(nx)dx)/(1−2λcosx +λ^2 )) 1) prove that λ u_(n+2) −(1+λ^2 )u_(n+1) +λ u_n =0 2) ptove that Σ u_n is convergent and find its sum

$${let}\:{give}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{cos}\left({nx}\right){dx}}{\mathrm{1}−\mathrm{2}\lambda{cosx}\:+\lambda^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\lambda\:{u}_{{n}+\mathrm{2}} \:−\left(\mathrm{1}+\lambda^{\mathrm{2}} \right){u}_{{n}+\mathrm{1}} \:+\lambda\:{u}_{{n}} =\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{ptove}\:{that}\:\Sigma\:{u}_{{n}} \:{is}\:{convergent}\:{and}\:{find}\:{its}\:{sum} \\ $$

Question Number 33124 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ (1/(n(n+1)2^(n−1) )) .

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\mathrm{2}^{{n}−\mathrm{1}} }\:. \\ $$

Question Number 32971 Answers: 1 Comments: 0

If siny=xsin(a+y) show that (dy/dx)=((sina)/(1−2xcosa+x^2 ))

$${If}\:{siny}={xsin}\left({a}+{y}\right)\:{show}\:{that} \\ $$$$\frac{{dy}}{{dx}}=\frac{{sina}}{\mathrm{1}−\mathrm{2}{xcosa}+{x}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 32968 Answers: 1 Comments: 0