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Question Number 89804 Answers: 1 Comments: 0

Question Number 89816 Answers: 0 Comments: 3

Question Number 89817 Answers: 0 Comments: 0

Question Number 89795 Answers: 1 Comments: 0

Question Number 89794 Answers: 0 Comments: 1

true or false (1+(1/1^3 ))(1+(1/2^3 ))(1+(1/3^3 )).....(1+(1/n^3 ))<3

$${true}\:{or}\:{false} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right).....\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{3}} }\right)<\mathrm{3} \\ $$

Question Number 89781 Answers: 0 Comments: 8

Question Number 89776 Answers: 0 Comments: 2

what is the stability of the following function (dy/dt) = y^3 −2y^2 + y

$${what}\:{is}\:{the}\:{stability}\:{of}\:{the}\: \\ $$$${following}\:{function}\: \\ $$$$\frac{{dy}}{{dt}}\:=\:{y}^{\mathrm{3}} \:−\mathrm{2}{y}^{\mathrm{2}} \:+\:{y}\: \\ $$

Question Number 89768 Answers: 2 Comments: 0

t(n) − t(n−1) = n for n > 0 and t(0) = 1 find t(n)

$${t}\left({n}\right)\:−\:{t}\left({n}−\mathrm{1}\right)\:=\:{n}\:\: \\ $$$${for}\:{n}\:>\:\mathrm{0}\:{and}\:{t}\left(\mathrm{0}\right)\:=\:\mathrm{1}\: \\ $$$${find}\:{t}\left({n}\right)\: \\ $$

Question Number 89755 Answers: 1 Comments: 1

Question Number 89753 Answers: 1 Comments: 6

(d/dx) (Π_(k = 1) ^(16) (x+(1/k)))∣_( x = 0) = ?

$$\frac{\mathrm{d}}{\mathrm{dx}}\:\left(\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{16}} {\prod}}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{k}}\right)\right)\underset{\:\mathrm{x}\:=\:\mathrm{0}} {\mid}\:=\:? \\ $$

Question Number 89749 Answers: 0 Comments: 4

Question Number 89748 Answers: 0 Comments: 4

dx = (1+2xtan y) dy

$$\mathrm{dx}\:=\:\left(\mathrm{1}+\mathrm{2xtan}\:\mathrm{y}\right)\:\mathrm{dy}\: \\ $$

Question Number 89745 Answers: 0 Comments: 2

f(x) = f(x+((3π)/8)) , ∀x∈ R if ∫_0 ^(3π/8) f(x) dx = t , then ∫_π ^(5π/2) f(x−π) dx = A. 2t B. 3t C. 4t D. 6t E. 8t

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:,\:\forall\mathrm{x}\in\:\mathbb{R} \\ $$$$\mathrm{if}\:\underset{\mathrm{0}} {\overset{\mathrm{3}\pi/\mathrm{8}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{t}\:,\:\mathrm{then}\: \\ $$$$\underset{\pi} {\overset{\mathrm{5}\pi/\mathrm{2}} {\int}}\mathrm{f}\left(\mathrm{x}−\pi\right)\:\mathrm{dx}\:=\: \\ $$$$\mathrm{A}.\:\mathrm{2t}\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{3t}\:\:\:\:\:\:\:\mathrm{C}.\:\mathrm{4t}\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{6t} \\ $$$$\mathrm{E}.\:\mathrm{8t}\: \\ $$

Question Number 89920 Answers: 0 Comments: 1

x=(1/(1+(1/(1+x)))) and y=(2/(2+(1/(1+y )))) find x+y

$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$

Question Number 89741 Answers: 0 Comments: 1

Question Number 89737 Answers: 0 Comments: 0

Question Number 89736 Answers: 0 Comments: 1

Question Number 89735 Answers: 0 Comments: 1

Question Number 89732 Answers: 0 Comments: 0

Question Number 89728 Answers: 1 Comments: 0

Find the area bounded by 3x+4y=12 and the coordinate axes?

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{12} \\ $$$${and}\:{the}\:{coordinate}\:{axes}? \\ $$

Question Number 89726 Answers: 0 Comments: 0

∫_0 ^1 6(√(x/(x^2 +1))) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{6}\sqrt{\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{1}}}\:{dx} \\ $$

Question Number 89719 Answers: 0 Comments: 0

find ∫_1 ^(+∞) ((arctan(ln(x)))/(4+x^2 ))dx

$${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left({ln}\left({x}\right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 89718 Answers: 0 Comments: 0

let f(x)=(√(2x+1))−(√(2x−1)) find f^((n)) by recurence

$${let}\:{f}\left({x}\right)=\sqrt{\mathrm{2}{x}+\mathrm{1}}−\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$$${find}\:{f}^{\left({n}\right)} \:{by}\:{recurence} \\ $$

Question Number 89717 Answers: 1 Comments: 0

let f(x)=2x−(√(x−1)) find ∫ ((f^(−1) (x))/(f(x)))dx

$${let}\:\:{f}\left({x}\right)=\mathrm{2}{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\: \\ $$

Question Number 89716 Answers: 0 Comments: 0

calculate A_n =∫_0 ^∞ e^(−n[x]) sin((([x])/n))dx find nature of Σ n^2 A_n

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{n}\left[{x}\right]} \:{sin}\left(\frac{\left[{x}\right]}{{n}}\right){dx} \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{n}^{\mathrm{2}} \:{A}_{{n}} \\ $$

Question Number 89714 Answers: 1 Comments: 1

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

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

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