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Question Number 171091 Answers: 0 Comments: 2

Question Number 171090 Answers: 1 Comments: 3

I_n =∫_0 ^1 (1−u)(√(ud(u))) Demonstrate that ∀n∈N, I_(n+1) −I_n =(1−u)^n u^(3/2) d(u) and deduce the meaning of variations of (I_n )∈N

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)\sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} =\left(\mathrm{1}−{u}\right)^{{n}} {u}^{\frac{\mathrm{3}}{\mathrm{2}}} {d}\left({u}\right)\:\:{and}\:{deduce}\:{the}\:{meaning}\:{of}\:{variations}\:{of}\:\left({I}_{{n}} \right)\in{N} \\ $$

Question Number 171085 Answers: 1 Comments: 0

43 devided by x remainder is x−5 how many value of x?

$$\mathrm{43}\:{devided}\:{by}\:{x}\:{remainder}\:{is}\:{x}−\mathrm{5}\:{how}\:{many}\:{value}\:{of}\:{x}? \\ $$

Question Number 171079 Answers: 1 Comments: 2

lim_(x→0) (((√(1+(√(1+(√(1−x))))))−(√(1+(√(1+(√(1+x)))))))/x)=?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}}−\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}}}{{x}}=? \\ $$

Question Number 171078 Answers: 1 Comments: 0

sketch the graph of y=ln(x+5)

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{5}\right) \\ $$$$ \\ $$

Question Number 171071 Answers: 1 Comments: 0

justify that ∫_0 ^(+∞) (dt/(1+t^4 )) is convergent.

$${justify}\:{that}\:\int_{\mathrm{0}} ^{+\infty} \frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} }\:{is}\:{convergent}. \\ $$

Question Number 171070 Answers: 1 Comments: 0

x^2 −1=2^x find x

$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}=\mathrm{2}^{\boldsymbol{\mathrm{x}}} \\ $$$$\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 171064 Answers: 2 Comments: 0

When A^(−1) = [(3,1),(8,4) ] find the A=? ,∣A^(−1) ∣∙A=?

$${When}\:\:{A}^{−\mathrm{1}} =\begin{bmatrix}{\mathrm{3}}&{\mathrm{1}}\\{\mathrm{8}}&{\mathrm{4}}\end{bmatrix} \\ $$$${find}\:{the}\:\:{A}=?\:,\mid{A}^{−\mathrm{1}} \mid\centerdot{A}=? \\ $$

Question Number 171046 Answers: 2 Comments: 0

Question Number 171044 Answers: 1 Comments: 3

Is the Light a matter?

$${Is}\:{the}\:{Light}\:{a}\:{matter}? \\ $$

Question Number 171043 Answers: 1 Comments: 0

A∈R A=(((√(x−2))+x+3)/( (√(4−2x))+x−1)) faind A=?

$${A}\in{R} \\ $$$${A}=\frac{\sqrt{{x}−\mathrm{2}}+{x}+\mathrm{3}}{\:\sqrt{\mathrm{4}−\mathrm{2}{x}}+{x}−\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{faind}\:{A}=? \\ $$

Question Number 171034 Answers: 0 Comments: 2

Question Number 171033 Answers: 2 Comments: 1

lim_(x→0) (1/x) [ ((((1−(√(1−x)))/( (√(1+x))−1)) ))^(1/3) −1 ]=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\:\left[\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}−\mathrm{1}}\:}−\mathrm{1}\:\right]=? \\ $$

Question Number 171032 Answers: 1 Comments: 0

Find the domain and range of the function, f(x)=((x^2 +2)/(2x+1)) Mastermind

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function},\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171031 Answers: 1 Comments: 0

Question Number 171025 Answers: 2 Comments: 0

Question Number 171023 Answers: 0 Comments: 0

Question Number 171038 Answers: 2 Comments: 0

Question Number 171021 Answers: 0 Comments: 0

Question Number 171039 Answers: 1 Comments: 0

I_n =∫_0 ^1 (1−u)^n (√(ud(u))) Demonstrate that ∀n∈N, I_n ≥0

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)^{{n}} \sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}} \geq\mathrm{0} \\ $$

Question Number 176906 Answers: 1 Comments: 3

Question Number 171014 Answers: 1 Comments: 0

Question Number 182219 Answers: 1 Comments: 0

Question Number 171012 Answers: 1 Comments: 1

The number of five digits can be made with the digits 1, 2, 3 each of which can be used atmost thrice in a number is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}\:\mathrm{digits}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{used}\:\mathrm{atmost}\:\mathrm{thrice}\:\mathrm{in}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is} \\ $$

Question Number 171011 Answers: 2 Comments: 0

How many 5-digit numbers from the digits {0, 1, ....., 9} have? (i) Strictly increasing digits (ii) Strictly increasing or decreasing digits (iii) Increasing digits (iv) Increasing or decreasing digits

$$\mathrm{How}\:\mathrm{many}\:\mathrm{5}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{digits}\:\left\{\mathrm{0},\:\mathrm{1},\:.....,\:\mathrm{9}\right\}\:\mathrm{have}? \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{or}\:\mathrm{decreasing} \\ $$$$\mathrm{digits} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{iv}\right)\:\mathrm{Increasing}\:\mathrm{or}\:\mathrm{decreasing}\:\mathrm{digits} \\ $$

Question Number 176748 Answers: 2 Comments: 0

log_4 (√(8−x))=1−log_4 x solve for x

$${log}_{\mathrm{4}} \sqrt{\mathrm{8}−{x}}=\mathrm{1}−{log}_{\mathrm{4}} {x} \\ $$$${solve}\:{for}\:{x} \\ $$

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