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Question Number 114671 Answers: 1 Comments: 0

Integrate ∫ ((x^4 +x^(−4) )/(x^6 +x^(−6) ))dx

$$ \\ $$$$\:\mathrm{Integrate}\:\:\int\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{−\mathrm{4}} }{\mathrm{x}^{\mathrm{6}} +\mathrm{x}^{−\mathrm{6}} }\mathrm{dx} \\ $$

Question Number 114668 Answers: 1 Comments: 0

((x+(√(x^2 −1)))/(x−(√(x^2 −1)))) + ((x−(√(x^2 −1)))/(x+(√(x^2 −1)))) = 98

$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:+\:\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\mathrm{98}\: \\ $$

Question Number 114665 Answers: 1 Comments: 0

Question Number 114660 Answers: 1 Comments: 1

Question Number 114656 Answers: 1 Comments: 2

2tanx−1=1 ⇔2tanx=1+1 tanx=(2/2)=1

$$\mathrm{2}{tanx}−\mathrm{1}=\mathrm{1} \\ $$$$\Leftrightarrow\mathrm{2}{tanx}=\mathrm{1}+\mathrm{1} \\ $$$${tanx}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1} \\ $$

Question Number 114654 Answers: 2 Comments: 2

Question Number 114653 Answers: 2 Comments: 0

solve 6x^4 −25x^3 +12x^2 −25x+6=0

$${solve}\:\mathrm{6}{x}^{\mathrm{4}} −\mathrm{25}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} −\mathrm{25}{x}+\mathrm{6}=\mathrm{0} \\ $$

Question Number 114647 Answers: 0 Comments: 5

Question Number 114638 Answers: 1 Comments: 0

Given a = ((1^2 +2^2 +3^2 +...+16^2 −16)/(1.3+2.4+3.5+...+15.17)) c = (1−(1/2)).(1−(1/3)).(1−(1/4)).(1−(1/5)). (1+(1/5))(1+(1/4))(1+(1/3))(1+(1/2)). find a×c =

Question Number 114637 Answers: 1 Comments: 0

lim_(x→(π/2)) (((π/2)−cos^(−1) (2x−π))/(1−sin^(−1) (((2x)/π)))) ?

$$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\frac{\pi}{\mathrm{2}}−\mathrm{cos}\:^{−\mathrm{1}} \left(\mathrm{2}{x}−\pi\right)}{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\pi}\right)}\:? \\ $$

Question Number 114635 Answers: 1 Comments: 3

find ∫_0 ^1 x^4 ln(x)ln(1−x^2 )dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{4}} \mathrm{ln}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:\: \\ $$

Question Number 114627 Answers: 2 Comments: 0

sin A+sin 2A+sin 3A+...+sin nA =??

$$\mathrm{sin}\:{A}+\mathrm{sin}\:\mathrm{2}{A}+\mathrm{sin}\:\mathrm{3}{A}+...+\mathrm{sin}\:{nA}\:=?? \\ $$

Question Number 114625 Answers: 1 Comments: 0

Question Number 114615 Answers: 1 Comments: 0

Question Number 114597 Answers: 3 Comments: 0

What is the number value of f[((log((( (√(x )) − 1 )/(x − 1))) ))^(1/3) ] = (√((√(x )) + x )) for f(−1)? a) 0,1 b) 27 c) 81 d) 10 e) 12

Question Number 114593 Answers: 1 Comments: 0

((∣x−1∣)/(∣x∣−1)) ≤ 1

$$\frac{\mid{x}−\mathrm{1}\mid}{\mid{x}\mid−\mathrm{1}}\:\leqslant\:\mathrm{1} \\ $$

Question Number 114592 Answers: 3 Comments: 0

Solve : x^2 +2x−1≡0(mod 3)

$$\mathrm{Solve}\::\:{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$

Question Number 114586 Answers: 1 Comments: 2

f(x)−2f((1/2))=3x−2 f(x)=?

$$\mathrm{f}\left(\mathrm{x}\right)−\mathrm{2f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{3x}−\mathrm{2} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 114582 Answers: 0 Comments: 1

Question Number 114577 Answers: 1 Comments: 5

x=(π/(30)) ((cos14x×cos6x)/(cos4x))=?

$$\mathrm{x}=\frac{\pi}{\mathrm{30}} \\ $$$$\frac{\mathrm{cos14x}×\mathrm{cos6x}}{\mathrm{cos4x}}=? \\ $$

Question Number 114570 Answers: 2 Comments: 0

Given that N=625(1−(9/5^2 ))(1−(9/8^2 ))(1−(9/(11^2 )))...(1−(9/(125^2 ))) Find the sum of the digits of N.

$$\mathrm{Given}\:\mathrm{that}\: \\ $$$${N}=\mathrm{625}\left(\mathrm{1}−\frac{\mathrm{9}}{\mathrm{5}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{9}}{\mathrm{8}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{9}}{\mathrm{11}^{\mathrm{2}} }\right)...\left(\mathrm{1}−\frac{\mathrm{9}}{\mathrm{125}^{\mathrm{2}} }\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:{N}. \\ $$

Question Number 114567 Answers: 0 Comments: 1

Question Number 114566 Answers: 2 Comments: 0

Question Number 114561 Answers: 1 Comments: 0

Question Number 114554 Answers: 1 Comments: 0

Given a matrix A = (((a b)),((c d)) ) satisfies the equation A^2 +λA+7I = 0 where I= (((1 0)),((0 1)) ) . Find the value of trace of A

$${Given}\:{a}\:{matrix}\:{A}\:=\:\begin{pmatrix}{{a}\:\:\:{b}}\\{{c}\:\:\:{d}}\end{pmatrix}\:{satisfies} \\ $$$${the}\:{equation}\:{A}^{\mathrm{2}} +\lambda{A}+\mathrm{7}{I}\:=\:\mathrm{0} \\ $$$${where}\:{I}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}\:.\:{Find}\:{the}\:{value}\:{of}\: \\ $$$${trace}\:{of}\:{A}\: \\ $$

Question Number 114551 Answers: 1 Comments: 3

The value of x in the given equation 4^x −3^(x−(1/2)) = 3^(x+(1/2)) −2^(2x−1) , is _,

$${The}\:{value}\:{of}\:{x}\:{in}\:{the}\:{given}\:{equation} \\ $$$$\mathrm{4}^{{x}} −\mathrm{3}^{{x}−\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\mathrm{3}^{{x}+\frac{\mathrm{1}}{\mathrm{2}}} \:−\mathrm{2}^{\mathrm{2}{x}−\mathrm{1}} \:,\:{is}\:\_, \\ $$

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