Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 181

Question Number 193332    Answers: 0   Comments: 0

Question Number 193331    Answers: 0   Comments: 0

Question Number 193328    Answers: 1   Comments: 0

f(x)= { ((((x^2 −x)/(x^2 −1)) ; x≠1)),((2x+1; x=1)) :} thene find lim_(x→1) f(x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:;\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{1}}\\{\mathrm{2x}+\mathrm{1};\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{1}}\end{cases} \\ $$$$\mathrm{thene}\:\mathrm{find}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$

Question Number 193329    Answers: 0   Comments: 0

Question Number 193323    Answers: 1   Comments: 0

Question Number 193339    Answers: 1   Comments: 0

Prove that a group G of prime order is cyclic.

$${Prove}\:{that}\:{a}\:{group}\:{G}\:{of}\:{prime}\:{order}\:{is}\:{cyclic}. \\ $$$$ \\ $$

Question Number 193316    Answers: 2   Comments: 1

IS THIS RIGHT? I=∫_0 ^∞ e^(−ix^2 ) dx I^2 =∫_0 ^∞ e^(−ix^2 ) dx∫_0 ^∞ e^(−iy^2 ) dy =∫_0 ^∞ ∫_0 ^∞ e^(−iy^2 ) dye^(−ix^2 ) dx =∫_0 ^∞ ∫_0 ^∞ e^(−i(x^2 +y^2 )) dydx dydx=dA=rdrdθ I^2 =∫_0 ^(π/2) ∫_0 ^∞ e^(−ir^2 ) rdrdθ ∫_0 ^∞ e^(−ir^2 ) rdr; u=−ir^2 ⇒du=−2irdr −(i/2)∫_(−∞) ^0 e^u du=−(i/2) I^2 =∫_0 ^(π/2) −(i/2)dθ=−((iπ)/4)⇒I=(√((−iπ)/4)) I=(i/2)(√(e^(iπ/2) π))=((ie^(iπ/4) )/2)(√π) I=((i(√π))/2)(((√2)/2)(1+i))=((i(√(2π)))/4)(1+i)

$$ \\ $$$$\mathrm{IS}\:\mathrm{THIS}\:\mathrm{RIGHT}? \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{I}^{\mathrm{2}} =\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx}\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{iy}^{\mathrm{2}} } \mathrm{dy} \\ $$$$=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{iy}^{\mathrm{2}} } \mathrm{dye}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx} \\ $$$$=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{i}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)} \mathrm{dydx} \\ $$$$\mathrm{dydx}=\mathrm{dA}=\mathrm{rdrd}\theta \\ $$$$\mathrm{I}^{\mathrm{2}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ir}^{\mathrm{2}} } \mathrm{rdrd}\theta \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{ir}^{\mathrm{2}} } \mathrm{rdr};\:\mathrm{u}=−\mathrm{ir}^{\mathrm{2}} \Rightarrow\mathrm{du}=−\mathrm{2irdr} \\ $$$$−\frac{\mathrm{i}}{\mathrm{2}}\int_{−\infty} ^{\mathrm{0}} \mathrm{e}^{\mathrm{u}} \mathrm{du}=−\frac{\mathrm{i}}{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{I}^{\mathrm{2}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} −\frac{\mathrm{i}}{\mathrm{2}}\mathrm{d}\theta=−\frac{\mathrm{i}\pi}{\mathrm{4}}\Rightarrow\mathrm{I}=\sqrt{\frac{−\mathrm{i}\pi}{\mathrm{4}}} \\ $$$$\mathrm{I}=\frac{\mathrm{i}}{\mathrm{2}}\sqrt{\mathrm{e}^{\mathrm{i}\pi/\mathrm{2}} \pi}=\frac{\mathrm{ie}^{\mathrm{i}\pi/\mathrm{4}} }{\mathrm{2}}\sqrt{\pi} \\ $$$$\mathrm{I}=\frac{\mathrm{i}\sqrt{\pi}}{\mathrm{2}}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)\right)=\frac{\mathrm{i}\sqrt{\mathrm{2}\pi}}{\mathrm{4}}\left(\mathrm{1}+\mathrm{i}\right) \\ $$

Question Number 193314    Answers: 1   Comments: 0

a ,b, c > 0 & a^2 +b^2 +c^2 =3 prove that (((1+(3/(ab+bc+ca)) )^((a+b+c)^2 ) ))^(1/3) ≤(1+(a/b))(1+(b/c))(1+(c/a))

$$ \\ $$$$\boldsymbol{{a}}\:,\boldsymbol{{b}},\:\boldsymbol{{c}}\:\:>\:\mathrm{0}\:\&\:\:\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} =\mathrm{3}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\: \\ $$$$\sqrt[{\mathrm{3}}]{\left(\mathrm{1}+\frac{\mathrm{3}}{\boldsymbol{{ab}}+\boldsymbol{{bc}}+\boldsymbol{{ca}}}\:\right)^{\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} } \:}\leqslant\left(\mathrm{1}+\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{b}}}{\boldsymbol{{c}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{c}}}{\boldsymbol{{a}}}\right) \\ $$

Question Number 193309    Answers: 0   Comments: 1

Question Number 193307    Answers: 0   Comments: 0

Question Number 193296    Answers: 2   Comments: 1

If a^2 + b^2 + c^2 = 16, x^2 + y^2 + z^2 = 25 and ax + by + cz = 20 then what is the value of ((a + b + c)/(x + y + z)) ?

$$\mathrm{If}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:=\:\mathrm{16},\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:=\:\mathrm{25} \\ $$$$\mathrm{and}\:{ax}\:+\:{by}\:+\:{cz}\:=\:\mathrm{20}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\frac{{a}\:+\:{b}\:+\:{c}}{{x}\:+\:{y}\:+\:{z}}\:? \\ $$

Question Number 193295    Answers: 2   Comments: 0

Find the value of x from the following equations: 4^((x/y) + (y/x)) = 32 log_3 (x − y) + log_3 (x + y) = 1

$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}} \\ $$$$\boldsymbol{\mathrm{equations}}: \\ $$$$\mathrm{4}^{\frac{{x}}{{y}}\:+\:\frac{{y}}{{x}}} \:=\:\mathrm{32} \\ $$$$\mathrm{log}_{\mathrm{3}} \left({x}\:−\:{y}\right)\:+\:\mathrm{log}_{\mathrm{3}} \left({x}\:+\:{y}\right)\:=\:\mathrm{1} \\ $$

Question Number 193294    Answers: 0   Comments: 0

Question Number 193293    Answers: 1   Comments: 0

Question Number 193292    Answers: 1   Comments: 0

(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same color. (b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?

$$ \\ $$(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same color. (b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?

Question Number 193286    Answers: 1   Comments: 2

Let ′P′ is a prime number (P > 1000). If ′P′ devided by 1000, then remainder is ′r′. How many value of ′r′ ?

$$\mathrm{Let}\:'\mathrm{P}'\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\left(\mathrm{P}\:>\:\mathrm{1000}\right). \\ $$$$\mathrm{If}\:\:'\mathrm{P}'\:\mathrm{devided}\:\mathrm{by}\:\mathrm{1000},\:\mathrm{then}\:\mathrm{remainder}\:\mathrm{is}\:'\mathrm{r}'. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{value}\:\mathrm{of}\:\:'\mathrm{r}'\:? \\ $$

Question Number 193284    Answers: 1   Comments: 0

6y −2xy = 4 8z − yz = 9 10x − 4xz = 8 find x+y +z = ?

$$\:\:\:\mathrm{6}{y}\:−\mathrm{2}{xy}\:=\:\mathrm{4} \\ $$$$\:\:\:\:\mathrm{8}{z}\:−\:{yz}\:=\:\mathrm{9} \\ $$$$\:\:\:\mathrm{10}{x}\:−\:\mathrm{4}{xz}\:=\:\mathrm{8}\: \\ $$$${find}\:{x}+{y}\:+{z}\:=\:? \\ $$

Question Number 193280    Answers: 1   Comments: 0

Question Number 193278    Answers: 1   Comments: 0

Please Help...!! ∫^( ∞) _( 0) x.e^(−x) .sinx.dx

$${Please}\:{Help}...!! \\ $$$$\:\:\:\:\underset{\:\:\:\:\mathrm{0}} {\int}^{\:\:\infty} {x}.{e}^{−{x}} .{sinx}.{dx}\: \\ $$$$ \\ $$

Question Number 193272    Answers: 2   Comments: 0

Question Number 193268    Answers: 1   Comments: 0

Question Number 193267    Answers: 1   Comments: 0

Question Number 193266    Answers: 0   Comments: 0

Question Number 193262    Answers: 1   Comments: 0

lim_(x→+∞) (ln((x+(√(x^2 +1)))/(x+(√(x^2 −1)))).ln^2 ((x+1)/(x−1)))

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left({ln}\frac{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}.{ln}^{\mathrm{2}} \:\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right) \\ $$$$ \\ $$

Question Number 193256    Answers: 1   Comments: 0

Question Number 193253    Answers: 1   Comments: 0

Select the correct option with explaination: If (1/3)log_3 M + 3log_3 N = 1 + log_(0.008) 5 then a. M^9 = (9/N) b. N^9 = (9/M) c. M^3 = (3/N) d. N^3 = (3/M)

$$\boldsymbol{\mathrm{Select}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}\:\boldsymbol{\mathrm{with}}\: \\ $$$$\boldsymbol{\mathrm{explaination}}: \\ $$$$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{log}_{\mathrm{3}} {M}\:+\:\mathrm{3log}_{\mathrm{3}} {N}\:=\:\mathrm{1}\:+\:\mathrm{log}_{\mathrm{0}.\mathrm{008}} \mathrm{5}\:\mathrm{then} \\ $$$$\mathrm{a}.\:{M}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{N}} \\ $$$$\mathrm{b}.\:{N}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{M}} \\ $$$$\mathrm{c}.\:{M}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{N}} \\ $$$$\mathrm{d}.\:{N}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{M}}\: \\ $$

  Pg 176      Pg 177      Pg 178      Pg 179      Pg 180      Pg 181      Pg 182      Pg 183      Pg 184      Pg 185   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com