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Question Number 19953 Answers: 0 Comments: 0

Question Number 19920 Answers: 0 Comments: 2

lim_(n→∞) n∫_0 ^∞ sin x^n dx

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}\int_{\mathrm{0}} ^{\infty} \mathrm{sin}\:{x}^{{n}} \mathrm{d}{x} \\ $$

Question Number 19914 Answers: 0 Comments: 0

Question Number 19912 Answers: 1 Comments: 1

Question Number 19905 Answers: 0 Comments: 2

am get a trou ble to decrea se the size of text! where c an i able to de crease the size of text?

$$\mathrm{am}\:\mathrm{get}\:\mathrm{a}\:\mathrm{trou} \\ $$$$\mathrm{ble}\:\mathrm{to}\:\mathrm{decrea} \\ $$$$\mathrm{se}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\: \\ $$$$\mathrm{text}!\:\mathrm{where}\:\mathrm{c} \\ $$$$\mathrm{an}\:\mathrm{i}\:\mathrm{able}\:\mathrm{to}\:\mathrm{de} \\ $$$$\mathrm{crease}\:\mathrm{the}\:\mathrm{size} \\ $$$$\mathrm{of}\:\mathrm{text}? \\ $$

Question Number 19915 Answers: 2 Comments: 3

Question Number 19903 Answers: 1 Comments: 0

by use the first principle,find dy/dx of y=cos(x−(Π/8))

$$\mathrm{by}\:\mathrm{use}\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{principle},\mathrm{find} \\ $$$$\mathrm{dy}/\mathrm{dx}\:\mathrm{of}\: \\ $$$$\mathrm{y}=\mathrm{cos}\left(\mathrm{x}−\frac{\Pi}{\mathrm{8}}\right) \\ $$

Question Number 19900 Answers: 2 Comments: 0

Prove that this is an identity in x: (((x−a)(x−b))/((c−a)(c−b)))+(((x−b)(x−c))/((a−b)(a−c)))+(((x−c)(x−a))/((b−c)(b−a)))=1

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{this}\:\mathrm{is}\:\mathrm{an}\:\mathrm{identity}\:\mathrm{in}\:{x}: \\ $$$$\frac{\left({x}−{a}\right)\left({x}−{b}\right)}{\left({c}−{a}\right)\left({c}−{b}\right)}+\frac{\left({x}−{b}\right)\left({x}−{c}\right)}{\left({a}−{b}\right)\left({a}−{c}\right)}+\frac{\left({x}−{c}\right)\left({x}−{a}\right)}{\left({b}−{c}\right)\left({b}−{a}\right)}=\mathrm{1} \\ $$

Question Number 19895 Answers: 1 Comments: 1

Question Number 19898 Answers: 2 Comments: 0

Simplify : i log (((x − i)/(x + i))).

$$\mathrm{Simplify}\::\:{i}\:\mathrm{log}\:\left(\frac{{x}\:−\:{i}}{{x}\:+\:{i}}\right). \\ $$

Question Number 19890 Answers: 1 Comments: 0

A man on top of a tower of height 35m throws a stone vertically upwards with a speed of 14m/s. Find: (i)the height above the ground, reached by the stone. (ii)the speed of the stone,when it reaches the ground.

$${A}\:{man}\:{on}\:{top}\:{of}\:{a}\:{tower}\:{of}\:{height} \\ $$$$\mathrm{35}{m}\:{throws}\:{a}\:{stone}\:{vertically} \\ $$$${upwards}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{14}{m}/{s}. \\ $$$${Find}: \\ $$$$\left({i}\right){the}\:{height}\:{above}\:{the}\:{ground}, \\ $$$${reached}\:{by}\:{the}\:{stone}. \\ $$$$\left({ii}\right){the}\:{speed}\:{of}\:{the}\:{stone},{when} \\ $$$${it}\:{reaches}\:{the}\:{ground}. \\ $$

Question Number 19886 Answers: 0 Comments: 1

Good morning sirs.Please is there any site or pdf that really explains motion(from equation of motion to Newton′s laws of motion)? if there is pls mrw1 ,ajfour ,123456 ,Tinkutara, mr b.e.h.i ,joel and others please help out;i really need to learn it. Thanks.

$${Good}\:{morning}\:{sirs}.{Please}\:{is} \\ $$$${there}\:{any}\:{site}\:{or}\:{pdf}\:{that}\:{really} \\ $$$${explains}\:{motion}\left({from}\:{equation}\right. \\ $$$${of}\:{motion}\:{to}\:{Newton}'{s}\:{laws}\:{of} \\ $$$$\left.{motion}\right)?\: \\ $$$${if}\:{there}\:{is}\:{pls} \\ $$$${mrw}\mathrm{1}\:,{ajfour}\:,\mathrm{123456}\:,{Tinkutara}, \\ $$$${mr}\:{b}.{e}.{h}.{i}\:,{joel}\:{and}\:{others}\:{please} \\ $$$${help}\:{out};{i}\:{really}\:{need}\:{to}\:{learn}\:{it}. \\ $$$$ \\ $$$${Thanks}. \\ $$$$ \\ $$

Question Number 19884 Answers: 1 Comments: 1

Question Number 19877 Answers: 0 Comments: 0

Question Number 19875 Answers: 1 Comments: 1

Question Number 19860 Answers: 1 Comments: 0

log_e (√(((1−cox)/(1+cosx)) differentiate w.r.t x))

$$\mathrm{log}_{{e}} \sqrt{\frac{\mathrm{1}−{cox}}{\mathrm{1}+{cosx}}\:\:\boldsymbol{{differentiate}}\:\boldsymbol{{w}}.\boldsymbol{{r}}.\boldsymbol{{t}}\:\boldsymbol{{x}}} \\ $$

Question Number 19859 Answers: 0 Comments: 1

(((√)1+x−(√)1−x)/((√)1+x−(√)1−x)) differentiate w.r.t x

$$\frac{\sqrt{}\mathrm{1}+{x}−\sqrt{}\mathrm{1}−{x}}{\sqrt{}\mathrm{1}+{x}−\sqrt{}\mathrm{1}−{x}}\:\:\boldsymbol{{differentiate}}\:\boldsymbol{{w}}.\boldsymbol{{r}}.\boldsymbol{{t}}\:\boldsymbol{{x}} \\ $$

Question Number 19857 Answers: 0 Comments: 3

proof that (a_− +b_− ).c_− =a_− .c_− +b_− .c_− or the distribiuting law of dot products

$${proof}\:{that}\:\left(\underset{−} {{a}}+\underset{−} {{b}}\right).\underset{−} {{c}}=\underset{−} {{a}}.\underset{−} {{c}}+\underset{−} {{b}}.\underset{−} {{c}} \\ $$$${or}\:{the}\:{distribiuting}\:{law}\:{of}\:{dot}\:{products} \\ $$$$ \\ $$

Question Number 19822 Answers: 1 Comments: 0

Question Number 19812 Answers: 1 Comments: 0

If tangent line of equation y = (x/(3 − x)) at x = a crossed line y = x at (b,b) Find b in terms of a

$$\mathrm{If}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{of}\:\mathrm{equation}\:{y}\:=\:\frac{{x}}{\mathrm{3}\:−\:{x}}\:\mathrm{at}\: \\ $$$${x}\:=\:{a}\:\mathrm{crossed}\:\mathrm{line}\:{y}\:=\:{x}\:\mathrm{at}\:\left({b},{b}\right) \\ $$$$\mathrm{Find}\:{b}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a} \\ $$

Question Number 19811 Answers: 0 Comments: 2

If f(x) = (x +1)g(x) − 2 and g(3) = 4 Find the remainder if f(x) divided by (x + 1)(x − 3)

$$\mathrm{If}\:{f}\left({x}\right)\:=\:\left({x}\:+\mathrm{1}\right){g}\left({x}\right)\:−\:\mathrm{2}\:\mathrm{and}\:{g}\left(\mathrm{3}\right)\:=\:\mathrm{4} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:{f}\left({x}\right)\:\mathrm{divided}\:\mathrm{by}\: \\ $$$$\left({x}\:+\:\mathrm{1}\right)\left({x}\:−\:\mathrm{3}\right) \\ $$

Question Number 19809 Answers: 1 Comments: 0

If sin θ+cosec θ=2, then sin^2 θ+cosec^2 θ is equal to

$$\mathrm{If}\:\mathrm{sin}\:\theta+\mathrm{cosec}\:\theta=\mathrm{2},\:\mathrm{then}\:\mathrm{sin}^{\mathrm{2}} \theta+\mathrm{cosec}^{\mathrm{2}} \theta \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 19978 Answers: 1 Comments: 0

Let f be a one-to-one function from the set of natural numbers to itself such that f(mn) = f(m)f(n) for all natural numbers m and n. What is the least possible value of f(999)?

$$\mathrm{Let}\:{f}\:\mathrm{be}\:\mathrm{a}\:\mathrm{one}-\mathrm{to}-\mathrm{one}\:\mathrm{function}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{to}\:\mathrm{itself} \\ $$$$\mathrm{such}\:\mathrm{that}\:{f}\left({mn}\right)\:=\:{f}\left({m}\right){f}\left({n}\right)\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{natural}\:\mathrm{numbers}\:{m}\:\mathrm{and}\:{n}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{999}\right)? \\ $$

Question Number 19799 Answers: 0 Comments: 2

For a natural number b, let N(b) denote the number of natural numbers a for which the equation x^2 + ax + b = 0 has integer roots. What is the smallest value of b for which N(b) = 20?

$$\mathrm{For}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:{b},\:\mathrm{let}\:{N}\left({b}\right)\:\mathrm{denote} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{numbers}\:{a}\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:=\:\mathrm{0}\:\mathrm{has} \\ $$$$\mathrm{integer}\:\mathrm{roots}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest} \\ $$$$\mathrm{value}\:\mathrm{of}\:{b}\:\mathrm{for}\:\mathrm{which}\:{N}\left({b}\right)\:=\:\mathrm{20}? \\ $$

Question Number 19796 Answers: 1 Comments: 1

Question Number 19795 Answers: 1 Comments: 0

One morning, each member of Manjul′s family drank an 8-ounce mixture of coffee and milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Manjul drank 1/7-th of the total amount of milk and 2/17-th of the total amount of coffee. How many people are there in Manjul′s family?

$$\mathrm{One}\:\mathrm{morning},\:\mathrm{each}\:\mathrm{member}\:\mathrm{of}\:\mathrm{Manjul}'\mathrm{s} \\ $$$$\mathrm{family}\:\mathrm{drank}\:\mathrm{an}\:\mathrm{8}-\mathrm{ounce}\:\mathrm{mixture}\:\mathrm{of} \\ $$$$\mathrm{coffee}\:\mathrm{and}\:\mathrm{milk}.\:\mathrm{The}\:\mathrm{amounts}\:\mathrm{of}\:\mathrm{coffee} \\ $$$$\mathrm{and}\:\mathrm{milk}\:\mathrm{varied}\:\mathrm{from}\:\mathrm{cup}\:\mathrm{to}\:\mathrm{cup},\:\mathrm{but} \\ $$$$\mathrm{were}\:\mathrm{never}\:\mathrm{zero}.\:\mathrm{Manjul}\:\mathrm{drank}\:\mathrm{1}/\mathrm{7}-\mathrm{th} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{milk}\:\mathrm{and}\:\mathrm{2}/\mathrm{17}-\mathrm{th} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{coffee}.\:\mathrm{How} \\ $$$$\mathrm{many}\:\mathrm{people}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{Manjul}'\mathrm{s} \\ $$$$\mathrm{family}? \\ $$

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