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AllQuestion and Answers: Page 1211

Question Number 93986 Answers: 2 Comments: 0

Question Number 93963 Answers: 0 Comments: 12

we have for quadratic equations x=((−b±(√(b^2 −4ac)))/(2a)) what about cubic equation is there any rules or ways to solve?

$${we}\:{have}\:{for}\:{quadratic}\:{equations} \\ $$$${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${what}\:{about}\:{cubic}\:{equation}\:{is}\:{there}\:{any} \\ $$$${rules}\:{or}\:{ways}\:{to}\:{solve}? \\ $$

Question Number 93959 Answers: 1 Comments: 0

∫(tan3x+sec3x)dx=

$$\int\left(\mathrm{tan3x}+\mathrm{sec3x}\right)\mathrm{dx}= \\ $$

Question Number 93958 Answers: 2 Comments: 1

∫((sinx−cosx)/(sinx+cosx))dx=

$$\int\frac{\mathrm{sinx}−\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}= \\ $$

Question Number 93957 Answers: 0 Comments: 9

log_((√(17))−(√2)) (((15)/(√(19+(√(136))))))x^2 − log_((√(19))−(√3)) ((1/(22−(√(228)))))x = 3 x = ?

$$\: \\ $$$$\:\mathrm{log}_{\sqrt{\mathrm{17}}−\sqrt{\mathrm{2}}} \left(\frac{\mathrm{15}}{\sqrt{\mathrm{19}+\sqrt{\mathrm{136}}}}\right)\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{log}_{\sqrt{\mathrm{19}}−\sqrt{\mathrm{3}}} \left(\frac{\mathrm{1}}{\mathrm{22}−\sqrt{\mathrm{228}}}\right)\mathrm{x}\:=\:\mathrm{3} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 93955 Answers: 1 Comments: 0

lim_(x→0) ((x^3 −sin^3 x)/x^5 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} } \\ $$

Question Number 93953 Answers: 2 Comments: 0

Question Number 93952 Answers: 1 Comments: 0

Express the following as functions of A: (i) sec(A−((3π)/2)) (ii) cosec(A−(π/2)) (iii) tan(A−((3π_ )/2)) (iv) cos(720°+A) (v) tan (A+π)

$${Express}\:{the}\:{following}\:{as}\:{functions} \\ $$$${of}\:\boldsymbol{{A}}: \\ $$$$\left(\mathrm{i}\right)\:{sec}\left({A}−\frac{\mathrm{3}\pi}{\mathrm{2}}\right)\:\:\left(\mathrm{ii}\right)\:{cosec}\left({A}−\frac{\pi}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{iii}\right)\:{tan}\left({A}−\frac{\mathrm{3}\pi_{} }{\mathrm{2}}\right)\:\:\left(\mathrm{iv}\right)\:{cos}\left(\mathrm{720}°+{A}\right) \\ $$$$\left(\mathrm{v}\right)\:{tan}\:\left({A}+\pi\right) \\ $$

Question Number 93950 Answers: 2 Comments: 0

Let ∗ be the binary operation on N given by a∗b=L.C.M. of a and b. Find (i) 5∗7 , 20∗16 (ii) is ∗ communitative? (iii) is ∗ associative? (iv)Find the identity of ∗ in N (v) which elements of N are invertible for the operation ∗?

$${Let}\:\ast\:{be}\:{the}\:{binary}\:{operation}\:{on}\:\mathrm{N} \\ $$$${given}\:{by}\:\mathrm{a}\ast\mathrm{b}=\mathrm{L}.\mathrm{C}.\mathrm{M}.\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{\mathrm{b}}.\:\mathrm{F}{ind} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{5}\ast\mathrm{7}\:,\:\:\mathrm{20}\ast\mathrm{16}\:\:\:\left(\mathrm{ii}\right)\:\mathrm{is}\:\ast\:{communitative}? \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{is}\:\ast\:{associative}? \\ $$$$\left(\mathrm{iv}\right)\mathrm{F}{ind}\:{the}\:{identity}\:{of}\:\ast\:{in}\:\boldsymbol{\mathrm{N}} \\ $$$$\left(\mathrm{v}\right)\:\mathrm{which}\:\mathrm{elements}\:\mathrm{of}\:\boldsymbol{\mathrm{N}}\:{are}\:{invertible} \\ $$$$\:\:\:\:\:\:\:{for}\:{the}\:{operation}\:\ast? \\ $$

Question Number 93941 Answers: 0 Comments: 2

Show that the function f(x)=e^(x ) is of Reimann within x∈[1;5] hence calculate ∫_1 ^5 e^x dx

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}\:} \:\mathrm{is}\:\mathrm{of}\:\mathrm{Reimann}\:\mathrm{within} \\ $$$$\mathrm{x}\in\left[\mathrm{1};\mathrm{5}\right]\:\mathrm{hence}\:\mathrm{calculate}\:\int_{\mathrm{1}} ^{\mathrm{5}} \mathrm{e}^{\mathrm{x}} \mathrm{dx} \\ $$

Question Number 93940 Answers: 0 Comments: 2

Question Number 93937 Answers: 0 Comments: 5

∫(1/(√(tan x)))dx=?

$$\int\frac{\mathrm{1}}{\sqrt{\mathrm{tan}\:{x}}}{dx}=? \\ $$

Question Number 93933 Answers: 0 Comments: 5

Let ∗′ be the binary operation on the set {1,2,3,4,5} defined by a∗′b=H.C.Fof a and b. Is the operation ∗′ same as the operation ∗ defined above? justify your answer.

$${Let}\:\ast'\:{be}\:{the}\:{binary}\:{operation}\:{on}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}\:{defined}\:{by}\:\mathrm{a}\ast'\mathrm{b}=\mathrm{H}.\mathrm{C}.\mathrm{F}{of}\:{a}\:{and}\:{b}.\: \\ $$$${Is}\:{the}\:{operation}\:\ast'\:{same}\:{as}\:{the}\:{operation}\:\ast\:{defined}\:{above}?\:{justify}\:{your}\:{answer}. \\ $$

Question Number 93916 Answers: 0 Comments: 2

Question Number 93911 Answers: 0 Comments: 8

number of digit of a number 2^(2016) and 5^(2016) is?

$$\mathrm{number}\:\mathrm{of}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{2}^{\mathrm{2016}} \:\mathrm{and}\:\mathrm{5}^{\mathrm{2016}} \:\mathrm{is}? \\ $$

Question Number 93908 Answers: 0 Comments: 2

calculste lim_(x→0) ∫_x ^(2x) ((arctan(xt))/(t+x))dt

$${calculste}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{arctan}\left({xt}\right)}{{t}+{x}}{dt} \\ $$

Question Number 93907 Answers: 2 Comments: 4

1) calculate A_n =∫_0 ^(π/2) cos^n x dx 2) calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^n )) n integr natural

$$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {x}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural} \\ $$

Question Number 93906 Answers: 0 Comments: 0

find ∫_0 ^∞ (e^(−cosx) /(x^2 +1))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{cosx}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 93904 Answers: 1 Comments: 0

∫_0 ^∞ (e^(−ax) −e^(−bx) ) dx

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\left({e}^{−{ax}} −{e}^{−{bx}} \right)\:{dx}\: \\ $$

Question Number 93900 Answers: 0 Comments: 0

y′′+2xy= y

$$\mathrm{y}''+\mathrm{2}{xy}=\:\mathrm{y} \\ $$

Question Number 93899 Answers: 0 Comments: 0

find a function f continue on [a,b] wich verify (∫_a ^b f(x)dx)^2 =∫_a ^b f^2 (x)dx

$${find}\:{a}\:{function}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{wich}\:{verify} \\ $$$$\left(\int_{{a}} ^{{b}} {f}\left({x}\right){dx}\right)^{\mathrm{2}} \:=\int_{{a}} ^{{b}} \:{f}^{\mathrm{2}} \left({x}\right){dx}\: \\ $$

Question Number 93898 Answers: 1 Comments: 1

let f(x)=2(√(3−x)) and g(x) =x^2 −2x +5 1) calculate fog(x) and determine D_(fog) 2) calculate ∫ fog(x)dx 3) calculate ∫ ((f^(−1) (x))/(f(x)))dx and ∫ ((f^(−1) og(x))/(fog(x)))dx

$${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{\mathrm{3}−{x}}\:{and}\:{g}\left({x}\right)\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:+\mathrm{5} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{fog}\left({x}\right)\:{and}\:{determine}\:{D}_{{fog}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int\:{fog}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\:{and}\:\:\int\:\frac{{f}^{−\mathrm{1}} {og}\left({x}\right)}{{fog}\left({x}\right)}{dx} \\ $$

Question Number 93892 Answers: 0 Comments: 3

let a_(n+1) =(√(2+(√a_n ))) a_0 =(√2) find lim_(n→∞) a_(n+1)

$${let} \\ $$$${a}_{{n}+\mathrm{1}} =\sqrt{\mathrm{2}+\sqrt{{a}_{{n}} }}\:\:\:\:\:\:{a}_{\mathrm{0}} =\sqrt{\mathrm{2}} \\ $$$${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}+\mathrm{1}} \\ $$

Question Number 93874 Answers: 1 Comments: 4

find k if the vector (1^ −2,k) in R^3 be a linear combination of the vectors (3,0,2) &(2,−1,−5)

$$\mathrm{find}\:\mathrm{k}\:\mathrm{if}\:\mathrm{the}\:\mathrm{vector}\:\left(\bar {\mathrm{1}}−\mathrm{2},\mathrm{k}\right)\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$$\mathrm{be}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{combination}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{vectors}\:\left(\mathrm{3},\mathrm{0},\mathrm{2}\right)\:\&\left(\mathrm{2},−\mathrm{1},−\mathrm{5}\right)\: \\ $$

Question Number 93873 Answers: 1 Comments: 1

find ∫_(−∞) ^∞ (dx/((x^2 +2x+4)^3 ))

$${find}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)^{\mathrm{3}} } \\ $$

Question Number 93869 Answers: 0 Comments: 2

∫ (dx/(1−tan^2 x)) ?

$$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:? \\ $$

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