Question and Answers Forum

AllQuestion and Answers: Page 1205

Question Number 94123 Answers: 0 Comments: 0

prove that ∫_0 ^∞ ((sin^(2n) (x))/x^2 )d=∫_0 ^∞ ((sin^(2n−1) (x))/x)dx

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{2}{n}} \left({x}\right)}{{x}^{\mathrm{2}} }{d}=\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{2}{n}−\mathrm{1}} \left({x}\right)}{{x}}{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 94114 Answers: 0 Comments: 1

Find ∫_( 1) ^( ∞) ((sin^2 x)/x^2 ) dx

$${Find}\:\:\:\underset{\:\mathrm{1}} {\int}\overset{\:\infty} {\:}\:\:\frac{\mathrm{sin}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\:\:{dx}\:\: \\ $$

Question Number 94110 Answers: 1 Comments: 2

Question Number 94025 Answers: 0 Comments: 5

LCM(a,(3/5)a)=3a ∧ HCF(a,(3/5)a)=(1/5)a a=?

$$\mathrm{LCM}\left({a},\frac{\mathrm{3}}{\mathrm{5}}{a}\right)=\mathrm{3}{a}\:\wedge\:\mathrm{HCF}\left({a},\frac{\mathrm{3}}{\mathrm{5}}{a}\right)=\frac{\mathrm{1}}{\mathrm{5}}{a} \\ $$$${a}=? \\ $$

Question Number 94020 Answers: 0 Comments: 4

Question Number 94383 Answers: 4 Comments: 0

Integrate: (i).∫ (1/(1+x^4 ))dx (ii).∫_β ^( α) (√((x−𝛂)(β−x))) dx (iii). ∫_0 ^( 1) ∫_0 ^( x^2 ) e^(y/x) dx dy

$$\boldsymbol{\mathrm{Integrate}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\int\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{4}} }\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{ii}}\right).\int_{\beta} ^{\:\alpha} \sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\alpha}\right)\left(\beta−\boldsymbol{\mathrm{x}}\right)}\:\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{iii}}\right).\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{y}}/\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}}\:\boldsymbol{\mathrm{dy}} \\ $$

Question Number 94098 Answers: 1 Comments: 1

Integrate: ∫ (( dx)/(a sin x+ b cos x))

$$\:\:\mathrm{Integrate}: \\ $$$$\:\:\int\:\frac{\:\:\mathrm{dx}}{\mathrm{a}\:\mathrm{sin}\:\mathrm{x}+\:\mathrm{b}\:\mathrm{cos}\:\mathrm{x}} \\ $$

Question Number 94097 Answers: 2 Comments: 1

find all integers n for which 13 ∣4(n^2 +1).

$$\mathrm{find}\:\mathrm{all}\:\mathrm{integers}\:{n}\:\:\mathrm{for}\:\mathrm{which}\:\:\mathrm{13}\:\mid\mathrm{4}\left({n}^{\mathrm{2}} +\mathrm{1}\right). \\ $$

Question Number 94119 Answers: 0 Comments: 1

∫ cot^(−1) ((√x)) dx

$$\int\:\mathrm{cot}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\: \\ $$

Question Number 94096 Answers: 1 Comments: 1

The result of adding the odd natural numbers is: 1 = 1 1 + 3=4 1 + 3+ 5 = 9 1 + 3 + 5 +7 = 16 1 + 3 + 5 + 7+9 = 25 show that from this result, Σ_(i=1) ^n (2i−1) = n^2 .

$$\mathrm{The}\:\mathrm{result}\:\mathrm{of}\:\mathrm{adding}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{is}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{3}=\mathrm{4} \\ $$$$\:\:\mathrm{1}\:+\:\mathrm{3}+\:\mathrm{5}\:=\:\mathrm{9} \\ $$$$\mathrm{1}\:+\:\mathrm{3}\:+\:\mathrm{5}\:+\mathrm{7}\:=\:\mathrm{16} \\ $$$$\mathrm{1}\:+\:\mathrm{3}\:+\:\mathrm{5}\:+\:\mathrm{7}+\mathrm{9}\:=\:\mathrm{25} \\ $$$$\:\mathrm{show}\:\mathrm{that}\:\mathrm{from}\:\mathrm{this}\:\mathrm{result},\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{2}{i}−\mathrm{1}\right)\:=\:{n}^{\mathrm{2}} . \\ $$

Question Number 94095 Answers: 0 Comments: 0

How many subgroups do Z_3 ⊕Z_(16 ) has? Justify.

$$\mathrm{How}\:\mathrm{many}\:\mathrm{subgroups}\:\mathrm{do}\:\mathrm{Z}_{\mathrm{3}} \oplus\mathrm{Z}_{\mathrm{16}\:} \:\mathrm{has}?\:\mathrm{Justify}. \\ $$

Question Number 94093 Answers: 0 Comments: 0

evaluate the inequality for n≥2 ((π/2)−(1/n))(1/(n)^(1/n) )<∫_(1/n) ^(π/2) ((sin(t)))^(1/n) dt

$${evaluate}\:{the}\:{inequality}\:{for}\:{n}\geqslant\mathrm{2} \\ $$$$\left(\frac{\pi}{\mathrm{2}}−\frac{\mathrm{1}}{{n}}\right)\frac{\mathrm{1}}{\sqrt[{{n}}]{{n}}}<\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt[{{n}}]{{sin}\left({t}\right)}{dt} \\ $$

Question Number 94117 Answers: 0 Comments: 8

Another update available to provide ability to bookmark.

$$\mathrm{Another}\:\mathrm{update}\:\mathrm{available}\:\mathrm{to} \\ $$$$\mathrm{provide}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{bookmark}. \\ $$

Question Number 93991 Answers: 1 Comments: 11

Question Number 93982 Answers: 0 Comments: 7

LCM(a,(3/5)a)=3a a=?

$$\mathrm{LCM}\left({a},\frac{\mathrm{3}}{\mathrm{5}}{a}\right)=\mathrm{3}{a}\: \\ $$$${a}=? \\ $$

Question Number 93976 Answers: 1 Comments: 10

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

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

Pg 1200 Pg 1201 Pg 1202 Pg 1203 Pg 1204 Pg 1205 Pg 1206 Pg 1207 Pg 1208 Pg 1209

Contact: info@tinkutara.com