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AllQuestion and Answers: Page 1080

Question Number 107438 Answers: 1 Comments: 0

Question Number 107435 Answers: 0 Comments: 0

Question Number 107434 Answers: 0 Comments: 1

Question Number 107433 Answers: 1 Comments: 0

∫x^x dx=?

$$\int{x}^{{x}} {dx}=? \\ $$

Question Number 107432 Answers: 0 Comments: 0

Question Number 107428 Answers: 1 Comments: 1

The polynomial P(x)=x^3 +ax^2 −4x+b, where a and b are constants. Given that x−2 is a factor of P(x) and that a remainder of 6 is obtained when P(x) is divided by (x+1), find the values of a and b.

$$\mathrm{The}\:\mathrm{polynomial}\:{P}\left({x}\right)=\mathrm{x}^{\mathrm{3}} +\mathrm{ax}^{\mathrm{2}} −\mathrm{4x}+\mathrm{b}, \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{constants}.\:\mathrm{Given}\:\mathrm{that} \\ $$$$\mathrm{x}−\mathrm{2}\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:{P}\left({x}\right)\:\mathrm{and}\:\mathrm{that}\:\mathrm{a}\:\mathrm{remainder} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{is}\:\mathrm{obtained}\:\mathrm{when}\:{P}\left({x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\left(\mathrm{x}+\mathrm{1}\right),\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$

Question Number 107420 Answers: 1 Comments: 1

Question Number 107419 Answers: 1 Comments: 0

Factorize:−x^2 −2(√5)x+3

$${Factorize}:−\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\sqrt{\mathrm{5}}\boldsymbol{{x}}+\mathrm{3} \\ $$$$ \\ $$$$ \\ $$

Question Number 107415 Answers: 1 Comments: 1

Question Number 107414 Answers: 2 Comments: 0

⊚BeMath⊚ lim_(x→0) ((2−3cos^6 x cos^4 2x cos^2 4x+cos x)/(36x^2 ))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\circledcirc\mathcal{B}{e}\mathbb{M}{ath}\circledcirc \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}−\mathrm{3cos}\:^{\mathrm{6}} {x}\:\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{4}{x}+\mathrm{cos}\:{x}}{\mathrm{36}{x}^{\mathrm{2}} }\:\:\: \\ $$$$ \\ $$

Question Number 107403 Answers: 0 Comments: 0

Question Number 107401 Answers: 1 Comments: 0

sove y^(′′) =y^2

$$\mathrm{sove}\:\mathrm{y}^{''} \:=\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 107761 Answers: 0 Comments: 2

Question Number 107377 Answers: 2 Comments: 0

lim_(x→0) ((x(1+acos x)−bsin x)/x^3 ) = 1 Find a and b .

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}\left(\mathrm{1}+{a}\mathrm{cos}\:{x}\right)−{b}\mathrm{sin}\:{x}}{{x}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$${Find}\:\:{a}\:{and}\:{b}\:. \\ $$

Question Number 107373 Answers: 1 Comments: 0

(d^2 y/dx^2 )=((dy/dx))^n

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{n}} \\ $$

Question Number 107372 Answers: 2 Comments: 0

⋗Bobhans⋖ lim_(x→∞) x (√(((2x−cos 5x)/(3x^3 )) )) ?

$$\:\:\:\gtrdot\boldsymbol{\mathcal{B}\mathrm{obhans}}\lessdot \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\:\sqrt{\frac{\mathrm{2x}−\mathrm{cos}\:\mathrm{5x}}{\mathrm{3x}^{\mathrm{3}} }\:}\:? \\ $$

Question Number 107367 Answers: 0 Comments: 0

Question Number 107364 Answers: 4 Comments: 0

⊚BEMATH⊚ If tan x+sec x = b ⇒ cos x = ?

$$\:\:\:\:\:\:\circledcirc\mathscr{BEMATH}\circledcirc\: \\ $$$${If}\:\mathrm{tan}\:{x}+\mathrm{sec}\:{x}\:=\:{b}\:\Rightarrow\:\mathrm{cos}\:{x}\:=\:? \\ $$

Question Number 107362 Answers: 0 Comments: 1

∫_0 ^∞ x^π e^(−x) dx

$$\int_{\mathrm{0}} ^{\infty} \mathrm{x}^{\pi} \mathrm{e}^{−\mathrm{x}} \mathrm{dx} \\ $$

Question Number 107353 Answers: 2 Comments: 0

If a b 13 c d 25 are six consecutive terms of an AP .find tbe value of a b c and d.

$${If}\:\mathrm{a}\:\mathrm{b}\:\mathrm{13}\:\mathrm{c}\:\mathrm{d}\:\mathrm{25}\:\mathrm{are}\:\mathrm{six}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}{P}\:.{find}\:{tbe}\:{value}\:{of}\:{a}\:{b}\:{c}\:{and}\:{d}. \\ $$

Question Number 107350 Answers: 1 Comments: 0

Question Number 107342 Answers: 1 Comments: 0

Evaluate: χ:=∫_0 ^( (π/4)) x^2 tan(x)dx= ??? ★prepared by:★ ♣♣♣ M.N ♣♣♣

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{E}{valuate}: \\ $$$$\:\:\:\:\:\:\:\chi:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {x}^{\mathrm{2}} {tan}\left({x}\right){dx}=\:???\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\bigstar{prepared}\:{by}:\bigstar \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\clubsuit\clubsuit\clubsuit\:\:\:\mathscr{M}.\mathscr{N}\:\clubsuit\clubsuit\clubsuit \\ $$$$ \\ $$

Question Number 107385 Answers: 0 Comments: 7

⋰BeMath⋰ Given 6x^2 −6px+14p−2=0 has the roots are u & v where u,v ∉Z If u,v ≥ 1 , then the value of ∣u−v∣ . (a)14 (b)15 (c)16 (d)17 (e) 18

$$\:\:\:\:\:\iddots\mathcal{B}{e}\mathcal{M}{ath}\iddots \\ $$$${Given}\:\mathrm{6}{x}^{\mathrm{2}} −\mathrm{6}{px}+\mathrm{14}{p}−\mathrm{2}=\mathrm{0} \\ $$$${has}\:{the}\:{roots}\:{are}\:\:{u}\:\&\:{v}\:{where}\:{u},{v}\:\notin\mathbb{Z} \\ $$$${If}\:{u},{v}\:\geqslant\:\mathrm{1}\:,\:{then}\:{the}\:{value}\:{of}\:\mid{u}−{v}\mid\:. \\ $$$$\left({a}\right)\mathrm{14}\:\:\:\:\:\left({b}\right)\mathrm{15}\:\:\:\:\:\left({c}\right)\mathrm{16}\:\:\:\:\:\left({d}\right)\mathrm{17}\:\:\:\left({e}\right)\:\mathrm{18} \\ $$

Question Number 107352 Answers: 5 Comments: 0

⊚BeMath⊚ (1)1−(1/(√2)) +(1/(√3))−(1/(√4))+(1/(√5))−(1/(√6))+...=? (2) lim_(x→0) (1+sin x)^(1/x) ?

$$\:\:\:\:\:\:\:\:\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc \\ $$$$\left(\mathrm{1}\right)\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{4}}}+\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{6}}}+...=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:? \\ $$

Question Number 107331 Answers: 1 Comments: 0

If A is an invertible matrix, then det(A^(−1) ) is equal to

$$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{invertible}\:\mathrm{matrix},\:\mathrm{then}\:\mathrm{det}\left({A}^{−\mathrm{1}} \right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 107330 Answers: 2 Comments: 0

If a+b+c=0 one root of determinant (((a−x),( c),( b)),(( c),(b−x),( a)),(( b),( a),(c−x)))=0 is

$$\mathrm{If}\:\:\:{a}+{b}+{c}=\mathrm{0}\:\mathrm{one}\:\mathrm{root}\:\mathrm{of} \\ $$$$\begin{vmatrix}{{a}−{x}}&{\:\:\:\:{c}}&{\:\:\:{b}}\\{\:\:\:\:{c}}&{{b}−{x}}&{\:\:\:{a}}\\{\:\:\:\:{b}}&{\:\:\:{a}}&{{c}−{x}}\end{vmatrix}=\mathrm{0}\:\mathrm{is} \\ $$

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