Question and Answers Forum

AllQuestion and Answers: Page 995

Question Number 121199 Answers: 0 Comments: 0

Question Number 121188 Answers: 0 Comments: 0

N is written 158b687a in base 10. with a<b. show that N≡2+a[4]

$${N}\:{is}\:{written}\:\mathrm{158}{b}\mathrm{687}{a}\:{in}\:{base}\:\mathrm{10}. \\ $$$${with}\:\:{a}<{b}. \\ $$$${show}\:{that}\:{N}\equiv\mathrm{2}+{a}\left[\mathrm{4}\right] \\ $$

Question Number 121175 Answers: 1 Comments: 0

Question Number 121174 Answers: 4 Comments: 0

∫_(−π/2) ^(π/2) (x^2 +ln (((π+x)/(π−x))))cos x dx ?

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

Question Number 121172 Answers: 2 Comments: 0

lim_(x→∞) (((√(x^2 +1))−x+1)/(x+1)) ?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}+\mathrm{1}}{\mathrm{x}+\mathrm{1}}\:? \\ $$$$ \\ $$

Question Number 121170 Answers: 0 Comments: 0

(a;b;c)∈∀ a^a ∙ b^b ∙ c^c ≥(abc)^((a+b+c)/3)

$$\:\:\:\:\:\:\left(\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\right)\in\forall \\ $$$$\:\boldsymbol{{a}}^{\boldsymbol{{a}}} \centerdot\:\boldsymbol{{b}}^{\boldsymbol{{b}}} \centerdot\:\boldsymbol{{c}}^{\boldsymbol{{c}}} \geqslant\left(\boldsymbol{{abc}}\right)^{\frac{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}}{\mathrm{3}}} \\ $$

Question Number 121154 Answers: 4 Comments: 0

Question Number 121152 Answers: 0 Comments: 0

Question Number 121138 Answers: 2 Comments: 0

Question Number 121136 Answers: 2 Comments: 1

Question Number 121134 Answers: 2 Comments: 0

Question Number 121127 Answers: 3 Comments: 0

(√(3+2i))=?

$$\sqrt{\mathrm{3}+\mathrm{2}{i}}=? \\ $$

Question Number 121123 Answers: 1 Comments: 0

two cars moving at speed of 10(m/(sec)) and 16(m/(sec)) on a road with a length of 200m against each other so how long will it take them to reach each other?

$${two}\:{cars}\:{moving}\:{at}\:{speed}\:{of}\:\mathrm{10}\frac{{m}}{{sec}}\:{and}\: \\ $$$$\mathrm{16}\frac{{m}}{{sec}}\:{on}\:{a}\:{road}\:{with}\:{a}\:{length}\:{of}\:\mathrm{200}{m} \\ $$$${against}\:{each}\:{other}\:{so}\:{how}\:{long}\:{will} \\ $$$${it}\:{take}\:{them}\:{to}\:{reach}\:{each}\:{other}? \\ $$

Question Number 121119 Answers: 4 Comments: 0

M= ∫ _(−15) ^(−8) ( (dx/(x(√(1−x))))) ?

$$\mathrm{M}=\:\int\underset{−\mathrm{15}} {\overset{−\mathrm{8}} {\:}}\left(\:\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{1}−\mathrm{x}}}\right)\:?\: \\ $$

Question Number 121117 Answers: 2 Comments: 0

J=∫_0 ^3 ((2x^2 +x−1)/( (√(x+1)))) dx ?

$$\:\mathrm{J}=\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{\mathrm{2x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx}\:? \\ $$

Question Number 121111 Answers: 0 Comments: 7

Question Number 121102 Answers: 2 Comments: 0

∫ (((x−1)(√(x^4 +2x^3 −x^2 +2x+1)))/(x^2 (x+1))) dx ?

$$\:\int\:\frac{\left(\mathrm{x}−\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dx}\:? \\ $$

Question Number 121100 Answers: 1 Comments: 0

Question Number 121099 Answers: 1 Comments: 0

Let α be a root of x^5 −x^3 +x−2=0 Then prove that [α^6 ]=3 where[λ] denotes greatest integer less than or equal λ

$${Let}\:\alpha\:{be}\:{a}\:{root}\:{of}\:\:{x}^{\mathrm{5}} −{x}^{\mathrm{3}} +{x}−\mathrm{2}=\mathrm{0} \\ $$$${Then}\:{prove}\:{that}\:\:\:\left[\alpha^{\mathrm{6}} \right]=\mathrm{3}\:\:\:\:\:\:\:{where}\left[\lambda\right]\:\:{denotes}\:{greatest}\:{integer} \\ $$$${less}\:{than}\:{or}\:\:{equal}\:\lambda \\ $$

Question Number 121097 Answers: 1 Comments: 0

Question Number 121092 Answers: 0 Comments: 0

Question Number 121091 Answers: 0 Comments: 1

Question Number 121085 Answers: 3 Comments: 1

Question Number 121081 Answers: 0 Comments: 1

Question Number 121077 Answers: 5 Comments: 1

Question Number 121074 Answers: 2 Comments: 0

lim_(x→1) ((x−1)/( (√(x^2 −1))))?

$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}? \\ $$

Pg 990 Pg 991 Pg 992 Pg 993 Pg 994 Pg 995 Pg 996 Pg 997 Pg 998 Pg 999

Contact: [email protected]