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Question Number 81911 Answers: 1 Comments: 4

Question Number 81910 Answers: 0 Comments: 1

a_1 =1 a_2 =2 a_(n+1) =(n+1)a_n −2a_(n−1) find a_n =?

$${a}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){a}_{{n}} −\mathrm{2}{a}_{{n}−\mathrm{1}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 81906 Answers: 0 Comments: 1

Question Number 81889 Answers: 1 Comments: 0

Question Number 81888 Answers: 1 Comments: 1

Question Number 81887 Answers: 0 Comments: 2

Question Number 81884 Answers: 0 Comments: 1

Question Number 81879 Answers: 0 Comments: 2

The value of determinant determinant (((−1),( 1),( 1)),(( 1),(−1),( 1)),(( 1),( 1),(−1))) is equal to

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{determinant}\begin{vmatrix}{−\mathrm{1}}&{\:\:\:\:\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\:\:\:\:\mathrm{1}}&{−\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\:\:\:\:\mathrm{1}}&{\:\:\:\:\:\mathrm{1}}&{−\mathrm{1}}\end{vmatrix} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 81876 Answers: 0 Comments: 1

The system of linear equations x+y+z=2, 2x+y−z=3, 3x+2y+kz=4 has a unique solution if

$$\mathrm{The}\:\mathrm{system}\:\mathrm{of}\:\mathrm{linear}\:\mathrm{equations}\:{x}+{y}+{z}=\mathrm{2}, \\ $$$$\mathrm{2}{x}+{y}−{z}=\mathrm{3},\:\mathrm{3}{x}+\mathrm{2}{y}+{kz}=\mathrm{4}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique} \\ $$$$\mathrm{solution}\:\mathrm{if} \\ $$

Question Number 81892 Answers: 5 Comments: 0

Question Number 81874 Answers: 0 Comments: 2

If A= [(( 1),(−5),( 7)),(( 0),( 7),( 9)),((11),( 8),( 9)) ] then trace of matrix A is

$$\mathrm{If}\:{A}=\begin{bmatrix}{\:\:\mathrm{1}}&{−\mathrm{5}}&{\:\:\:\mathrm{7}}\\{\:\:\mathrm{0}}&{\:\:\:\:\mathrm{7}}&{\:\:\:\mathrm{9}}\\{\mathrm{11}}&{\:\:\:\:\mathrm{8}}&{\:\:\:\mathrm{9}}\end{bmatrix}\:\mathrm{then}\:\mathrm{trace}\:\mathrm{of}\: \\ $$$$\mathrm{matrix}\:{A}\:\mathrm{is} \\ $$

Question Number 81873 Answers: 1 Comments: 1

determinant (((sin^2 x),(cos^2 x),1),((cos^2 x),(sin^2 x),1),((−10),( 12),2))=

$$\begin{vmatrix}{\mathrm{sin}^{\mathrm{2}} {x}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{1}}\\{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{sin}^{\mathrm{2}} {x}}&{\mathrm{1}}\\{−\mathrm{10}}&{\:\:\mathrm{12}}&{\mathrm{2}}\end{vmatrix}= \\ $$

Question Number 81872 Answers: 1 Comments: 0

If every element of a third order determinant of value △ is multiplied by 5, then the value of new determinant is

$$\mathrm{If}\:\mathrm{every}\:\mathrm{element}\:\mathrm{of}\:\mathrm{a}\:\mathrm{third}\:\mathrm{order} \\ $$$$\mathrm{determinant}\:\mathrm{of}\:\mathrm{value}\:\bigtriangleup\:\mathrm{is}\:\mathrm{multiplied}\:\mathrm{by} \\ $$$$\mathrm{5},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{new}\:\mathrm{determinant}\:\mathrm{is} \\ $$

Question Number 81871 Answers: 1 Comments: 3

a_1 =4 a_(n+1) =((4a_n +3)/(a_n +2)) find a_n =?

$${a}_{\mathrm{1}} =\mathrm{4} \\ $$$${a}_{{n}+\mathrm{1}} =\frac{\mathrm{4}{a}_{{n}} +\mathrm{3}}{{a}_{{n}} +\mathrm{2}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 81854 Answers: 1 Comments: 1

Question Number 81853 Answers: 1 Comments: 2

lim_(x→∞) {n ∫_0 ^1 (x^n /(x^3 +1)) dx } = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{{n}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}^{{n}} }{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}\:\right\}\:=\:? \\ $$

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 81836 Answers: 0 Comments: 0

Question Number 81835 Answers: 0 Comments: 1

Question Number 81829 Answers: 1 Comments: 2

Question Number 81828 Answers: 0 Comments: 0

Question Number 81824 Answers: 1 Comments: 0

Question Number 81821 Answers: 1 Comments: 0

Question Number 81804 Answers: 2 Comments: 1

Question Number 81801 Answers: 1 Comments: 1

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