Question and Answers Forum

AllQuestion and Answers: Page 1206

Question Number 92740 Answers: 0 Comments: 0

∫ ((ln(x))/(cos x)) dx ?

$$\int\:\frac{\mathrm{ln}\left({x}\right)}{\mathrm{cos}\:{x}}\:{dx}\:? \\ $$

Question Number 92729 Answers: 1 Comments: 0

if p_n is the product of the terms in the nth row of the pascal′s triangle find lim_(n→∞) ((p_(n−1) p_(n+1) )/((p_n )^2 ))

$${if}\:{p}_{{n}} \:{is}\:{the}\:{product}\:{of}\:{the}\:{terms}\:{in} \\ $$$${the}\:{nth}\:{row}\:{of}\:{the}\:{pascal}'{s}\:{triangle} \\ $$$${find} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\frac{{p}_{{n}−\mathrm{1}} {p}_{{n}+\mathrm{1}} }{\left({p}_{{n}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 92727 Answers: 1 Comments: 0

Solve: x^y = y^x ....... (i) 3^x = 15^y ...... (ii) x ≠ y, x, y ∈ R

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:=\:\:\mathrm{y}^{\mathrm{x}} \:\:\:\:\:.......\:\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{x}} \:\:=\:\:\mathrm{15}^{\mathrm{y}} \:\:\:\:......\:\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\mathrm{x}\:\:\neq\:\:\mathrm{y},\:\:\:\:\:\:\:\mathrm{x},\:\:\mathrm{y}\:\in\:\mathbb{R} \\ $$

Question Number 92723 Answers: 1 Comments: 0

Question Number 92717 Answers: 2 Comments: 5

Question Number 92708 Answers: 1 Comments: 0

solve the differential equations. (a) (x + 3y^2 )(d^2 y/dx^2 ) + 6y ((dy/dx))^2 + 2(dy/dx) + 2 = 0 (b) (2y−x)(d^2 y/dx^2 ) + 2((dy/dx))^2 −2 (dy/dx) + 2 = 0

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equations}. \\ $$$$\:\left(\mathrm{a}\right)\:\left({x}\:+\:\mathrm{3}{y}^{\mathrm{2}} \right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{6}{y}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:+\:\mathrm{2}\frac{{dy}}{{dx}}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{b}\right)\:\left(\mathrm{2}{y}−{x}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:−\mathrm{2}\:\frac{{dy}}{{dx}}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$

Question Number 92702 Answers: 2 Comments: 0

y′′+2y′−3y=e^x +e^(2x)

$${y}''+\mathrm{2}{y}'−\mathrm{3}{y}={e}^{{x}} +{e}^{\mathrm{2}{x}} \\ $$

Question Number 92701 Answers: 0 Comments: 3

Question Number 92700 Answers: 0 Comments: 0

∫_(−(π/2)) ^(π/2) ((tan (x^2 )dx)/x) ?

$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{tan}\:\left({x}^{\mathrm{2}} \right){dx}}{{x}}\:?\: \\ $$

Question Number 92691 Answers: 1 Comments: 3

find x in eq tan^(−1) (x)= cos^(−1) (x)

$$\mathrm{find}\:{x}\:{in}\:{eq}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 92687 Answers: 0 Comments: 0

In a Gregorian calendar, a year finishing with 00 is a leap year if only it′s vintage is divisible by 400. Also, the 1^(st) January 1900 was a Monday. 1\ Show that a year with the vintage finishing with 00 cannot begin on a Sunday 2\ Show that for a person born between 1900−2071, his 28 anniversary will occur on the same day of birth.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{Gregorian}\:\mathrm{calendar},\:\mathrm{a}\:\mathrm{year}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{is}\:\mathrm{a}\:\mathrm{leap}\:\mathrm{year}\:\mathrm{if}\:\mathrm{only}\:\mathrm{it}'\mathrm{s}\:\mathrm{vintage}\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{400}.\:\mathrm{Also},\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{January}\:\mathrm{1900}\:\mathrm{was}\:\mathrm{a} \\ $$$$\mathrm{Monday}. \\ $$$$\mathrm{1}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:\mathrm{year}\:\mathrm{with}\:\mathrm{the}\:\mathrm{vintage}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{cannot}\:\mathrm{begin}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Sunday} \\ $$$$\mathrm{2}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{a}\:\mathrm{person}\:\mathrm{born}\:\mathrm{between}\:\mathrm{1900}−\mathrm{2071}, \\ $$$$\mathrm{his}\:\mathrm{28}\:\mathrm{anniversary}\:\mathrm{will}\:\mathrm{occur}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{day}\:\mathrm{of}\:\mathrm{birth}. \\ $$

Question Number 92684 Answers: 1 Comments: 4

Question Number 92682 Answers: 0 Comments: 5

While uninstalling/reinstalling app please use backup/import to keep your saved equation on device. backup: before unintalling import: after reinstalling

$$\mathrm{While}\:\mathrm{uninstalling}/\mathrm{reinstalling}\:\mathrm{app} \\ $$$$\mathrm{please}\:\mathrm{use}\:\mathrm{backup}/\mathrm{import}\:\mathrm{to}\:\mathrm{keep} \\ $$$$\mathrm{your}\:\mathrm{saved}\:\mathrm{equation}\:\mathrm{on}\:\mathrm{device}. \\ $$$$\mathrm{backup}:\:\mathrm{before}\:\mathrm{unintalling} \\ $$$$\mathrm{import}:\:\mathrm{after}\:\mathrm{reinstalling} \\ $$

Question Number 92712 Answers: 0 Comments: 2

find m for fix function f(x)=(((m−1)x+3)/(x−1))

$${find}\:\:\boldsymbol{{m}}\:{for}\:{fix}\:{function} \\ $$$${f}\left({x}\right)=\frac{\left(\boldsymbol{{m}}−\mathrm{1}\right){x}+\mathrm{3}}{{x}−\mathrm{1}} \\ $$

Question Number 92673 Answers: 1 Comments: 2

Show that if 3 prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{3}\:\mathrm{prime}\:\mathrm{numbers},\:\mathrm{all}\:\mathrm{greater} \\ $$$$\mathrm{than}\:\mathrm{3},\:\mathrm{form}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\mathrm{then}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}. \\ $$

Question Number 92668 Answers: 1 Comments: 2

∫_0 ^p (√(x/(c−x))) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{p}} {\int}}\:\sqrt{\frac{\mathrm{x}}{\mathrm{c}−\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$

Question Number 92646 Answers: 0 Comments: 22