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Question Number 11172 Answers: 1 Comments: 0

Tangent to the curve (x+y)^3 =(x−y+2)^2 at (−1,1).

$$\mathrm{Tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} =\left(\mathrm{x}−\mathrm{y}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\mathrm{at}\:\left(−\mathrm{1},\mathrm{1}\right). \\ $$

Question Number 11183 Answers: 1 Comments: 0

Question Number 10547 Answers: 1 Comments: 0

A man can row a boat at 4 km/hr in still water. He rows the boat 2km upstream and 2km back to his starting place in 2 hours. How fast is the stream flowing ?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{at}\:\mathrm{4}\:\mathrm{km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}. \\ $$$$\mathrm{He}\:\mathrm{rows}\:\mathrm{the}\:\mathrm{boat}\:\mathrm{2km}\:\mathrm{upstream}\:\mathrm{and}\:\mathrm{2km}\:\mathrm{back}\:\mathrm{to} \\ $$$$\mathrm{his}\:\mathrm{starting}\:\mathrm{place}\:\mathrm{in}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{fast}\:\mathrm{is}\:\mathrm{the}\:\mathrm{stream} \\ $$$$\mathrm{flowing}\:? \\ $$

Question Number 11206 Answers: 3 Comments: 0

Question Number 11204 Answers: 0 Comments: 0

Question Number 11203 Answers: 1 Comments: 0

f(x)=((x/(x+1))−(x/(x−1)))^(−1) =−(((x+1)(x−1))/(2x)) g(x)=−(1/2)x why is f(x)≈g(x)?

$${f}\left({x}\right)=\left(\frac{{x}}{{x}+\mathrm{1}}−\frac{{x}}{{x}−\mathrm{1}}\right)^{−\mathrm{1}} =−\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{\mathrm{2}{x}} \\ $$$${g}\left({x}\right)=−\frac{\mathrm{1}}{\mathrm{2}}{x} \\ $$$$\: \\ $$$$\mathrm{why}\:\mathrm{is}\:{f}\left({x}\right)\approx{g}\left({x}\right)? \\ $$

Question Number 11196 Answers: 0 Comments: 2

Give an example each with justification,of a function defined by ]−1,1[ ,which is 1)one one but not onto. 2)onto but not one one.

$$\mathrm{Give}\:\mathrm{an}\:\mathrm{example}\:\mathrm{each}\:\mathrm{with}\:\mathrm{justification},\mathrm{of}\:\mathrm{a}\:\mathrm{function} \\ $$$$\left.\mathrm{defined}\:\mathrm{by}\:\right]−\mathrm{1},\mathrm{1}\left[\:,\mathrm{which}\:\mathrm{is}\right. \\ $$$$\left.\mathrm{1}\right)\mathrm{one}\:\mathrm{one}\:\mathrm{but}\:\mathrm{not}\:\mathrm{onto}. \\ $$$$\left.\mathrm{2}\right)\mathrm{onto}\:\mathrm{but}\:\mathrm{not}\:\mathrm{one}\:\mathrm{one}. \\ $$

Question Number 10544 Answers: 0 Comments: 1

The number of terms in the expansion of (1+2x+x^2 )^(20) when expanded in descending powers of x, is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+\mathrm{2}{x}+{x}^{\mathrm{2}} \right)^{\mathrm{20}} \mathrm{when}\:\mathrm{expanded}\:\mathrm{in}\:\mathrm{descending} \\ $$$$\mathrm{powers}\:\mathrm{of}\:{x},\:\mathrm{is} \\ $$

Question Number 10543 Answers: 0 Comments: 0

Question Number 10542 Answers: 1 Comments: 0

Prove that: tan(sec^(−1) ((√(tan(θ)))))=(√(tan(θ)))(√(1−cot(θ)))

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{tan}\left(\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\left(\theta\right)}\right)\right)=\sqrt{\mathrm{tan}\left(\theta\right)}\sqrt{\mathrm{1}−\mathrm{cot}\left(\theta\right)} \\ $$

Question Number 10540 Answers: 1 Comments: 3

Question Number 10539 Answers: 1 Comments: 0

prove that (√(2 + ^3 (√(3 +...+ ^(1993) (√(1993)))))) <2

$${prove}\:{that} \\ $$$$\sqrt{\mathrm{2}\:+\overset{\mathrm{3}} {\:}\sqrt{\mathrm{3}\:+...+\overset{\mathrm{1993}} {\:}\sqrt{\mathrm{1993}}}}\:<\mathrm{2} \\ $$

Question Number 10536 Answers: 1 Comments: 0

how can one rougly judge ((548)/(879)) ?

$${how}\:{can}\:{one}\:{rougly}\:\:{judge}\:\frac{\mathrm{548}}{\mathrm{879}}\:? \\ $$

Question Number 10521 Answers: 1 Comments: 0

A number (αβ..λ...μ2)×2 =(2αβ..λ...μ) find the number.

$${A}\:{number}\:\left(\alpha\beta..\lambda...\mu\mathrm{2}\right)×\mathrm{2}\:=\left(\mathrm{2}\alpha\beta..\lambda...\mu\right) \\ $$$${find}\:{the}\:{number}. \\ $$$$ \\ $$

Question Number 10517 Answers: 0 Comments: 0

Question Number 10515 Answers: 1 Comments: 0

2^a =6^((x/(x+y)) ) .3^a =6^(y/(x+y)) ⇒8^((y/x)+1) =?

$$\mathrm{2}^{{a}} =\mathrm{6}^{\frac{{x}}{{x}+{y}}\:} \:\:\:.\mathrm{3}^{{a}} \:=\mathrm{6}^{\frac{{y}}{{x}+{y}}} \:\Rightarrow\mathrm{8}^{\frac{{y}}{{x}}+\mathrm{1}} =? \\ $$

Question Number 10513 Answers: 0 Comments: 1

e^((−2×10^(−2) /2))

$${e}^{\left(−\mathrm{2}×\mathrm{10}^{−\mathrm{2}} /\mathrm{2}\right)} \\ $$

Question Number 10512 Answers: 0 Comments: 0

find C.I. and P.I. of differential equations . (d^2 y/dx^2 ) +4y=tan 2x.

$$\mathrm{find}\:\mathrm{C}.\mathrm{I}.\:\mathrm{and}\:\:\mathrm{P}.\mathrm{I}.\:\mathrm{of}\:\mathrm{differential}\:\mathrm{equations}\:. \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\mathrm{4y}=\mathrm{tan}\:\mathrm{2x}. \\ $$

Question Number 10510 Answers: 2 Comments: 0

Question Number 10507 Answers: 0 Comments: 0

Question Number 10528 Answers: 3 Comments: 0

Give the velocity field v = (6 + 2xy + t^2 )i − (xy^2 + 10t)j + 25k what is the acceleration of the particle at (3, 0, 2) at time t = 1.

$$\mathrm{Give}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{field} \\ $$$$\mathrm{v}\:=\:\left(\mathrm{6}\:+\:\mathrm{2xy}\:+\:\mathrm{t}^{\mathrm{2}} \right)\mathrm{i}\:−\:\left(\mathrm{xy}^{\mathrm{2}} \:+\:\mathrm{10t}\right)\mathrm{j}\:+\:\mathrm{25k} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{at}\:\left(\mathrm{3},\:\mathrm{0},\:\mathrm{2}\right) \\ $$$$\mathrm{at}\:\mathrm{time}\:\mathrm{t}\:=\:\mathrm{1}. \\ $$

Question Number 10495 Answers: 1 Comments: 0

∫_0 ^(2π) (√(R^2 +r^2 −2Rrcos θ)) dθ

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \sqrt{{R}^{\mathrm{2}} +{r}^{\mathrm{2}} −\mathrm{2}{Rr}\mathrm{cos}\:\theta}\:{d}\theta \\ $$

Question Number 10493 Answers: 2 Comments: 0

(1/(2!))+(2/(3!))+(3/(4!))+(4/(5!))+...+((17)/(18!))=?

$$\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{2}}{\mathrm{3}!}+\frac{\mathrm{3}}{\mathrm{4}!}+\frac{\mathrm{4}}{\mathrm{5}!}+...+\frac{\mathrm{17}}{\mathrm{18}!}=? \\ $$

Question Number 10492 Answers: 1 Comments: 0

3^(logx) −2^(logx−1) =2^(logx+1) −2×3^(logx−1) ⇒x=?

$$\mathrm{3}^{{logx}} −\mathrm{2}^{{logx}−\mathrm{1}} =\mathrm{2}^{{logx}+\mathrm{1}} −\mathrm{2}×\mathrm{3}^{{logx}−\mathrm{1}} \Rightarrow{x}=? \\ $$

Question Number 10489 Answers: 1 Comments: 0

The fifth, nineth, sixteenth terms of a linear sequence are consecutive terms of an exponential sequence . (1) Find the common difference of the linear sequence in terms of the first term (2) Show that 21^(th) , 37^(th) , 65^(th) terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is (3/4)

$$\mathrm{The}\:\mathrm{fifth},\:\mathrm{nineth},\:\mathrm{sixteenth}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{linear}\: \\ $$$$\mathrm{sequence}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{exponential} \\ $$$$\mathrm{sequence}\:. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{linear}\: \\ $$$$\mathrm{sequence}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{21}^{\mathrm{th}} ,\:\mathrm{37}^{\mathrm{th}} ,\:\mathrm{65}^{\mathrm{th}} \:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{linear} \\ $$$$\mathrm{sequence}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{exponential} \\ $$$$\mathrm{sequence}\:\mathrm{whose}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Question Number 10488 Answers: 1 Comments: 0

An exponential sequence of positive terms and a linear sequence have the same first term. the sum o their first term is 3, the sum of their second term is (3/2), and the sum of their third term is 6. find the sum of their fifth term.

$$\mathrm{An}\:\mathrm{exponential}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{terms}\:\mathrm{and}\:\mathrm{a} \\ $$$$\mathrm{linear}\:\mathrm{sequence}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{first}\:\mathrm{term}.\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{o}\:\mathrm{their}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is}\:\mathrm{3},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{second}\:\mathrm{term} \\ $$$$\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{2}},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{third}\:\mathrm{term}\:\mathrm{is}\:\mathrm{6}.\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{fifth}\:\mathrm{term}. \\ $$

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