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Question Number 158687 Answers: 1 Comments: 0

∀x∈R f(x)=f ′ (x) and f(0)=1 prove f(a+b)=f(a)×f(b)

$$\forall{x}\in{R}\:\:{f}\left({x}\right)={f}\:'\:\left({x}\right)\:\:\:\:\:\:{and}\:\:\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${prove}\:\:{f}\left({a}+{b}\right)={f}\left({a}\right)×{f}\left({b}\right) \\ $$

Question Number 158675 Answers: 2 Comments: 1

Question Number 158674 Answers: 0 Comments: 2

Question Number 158671 Answers: 0 Comments: 3

∀x∈R ; f(x)=f ′(x) prove f(x+y)=f(x)f(y)

$$\forall{x}\in{R}\:;\:{f}\left({x}\right)={f}\:'\left({x}\right) \\ $$$${prove}\:{f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right) \\ $$

Question Number 158668 Answers: 1 Comments: 0

f(f(x))= (9x^2 +6x+2)f(x) f(x)=?

$$\:{f}\left({f}\left({x}\right)\right)=\:\left(\mathrm{9}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{2}\right){f}\left({x}\right) \\ $$$$\:{f}\left({x}\right)=? \\ $$

Question Number 158664 Answers: 2 Comments: 3

Question Number 158644 Answers: 1 Comments: 2

Solve for real numbers: 2^x + 2^(1 + (1/( (√x)))) = 6

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}^{\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}}}} \:=\:\mathrm{6} \\ $$$$ \\ $$

Question Number 158638 Answers: 0 Comments: 0

Provd that 2017^n can be written as the sum of seven perfect squares.

$$\mathrm{Provd}\:\mathrm{that}\:\:\mathrm{2017}^{\boldsymbol{\mathrm{n}}} \:\:\mathrm{can}\:\mathrm{be}\:\mathrm{written} \\ $$$$\mathrm{as}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{seven}\:\mathrm{perfect}\:\mathrm{squares}. \\ $$$$ \\ $$

Question Number 158636 Answers: 0 Comments: 3

Question Number 158711 Answers: 2 Comments: 2

Question Number 158630 Answers: 0 Comments: 0

Question Number 158685 Answers: 0 Comments: 1

Question Number 158622 Answers: 1 Comments: 1

Question Number 158781 Answers: 2 Comments: 0

Question Number 158780 Answers: 2 Comments: 0

Question Number 158619 Answers: 2 Comments: 1

Question Number 158598 Answers: 2 Comments: 2

Question Number 158694 Answers: 1 Comments: 0

Help me sir in phase sppace d^3 p=dp_x dp_(y ) dp_z then find ∫_0 ^∞ P^(2 ) e^(p^2 /(2mKT )) d^3 p =....

$${Help}\:{me}\:{sir} \\ $$$$\: \\ $$$${in}\:{phase}\:{sppace}\:\:{d}^{\mathrm{3}} {p}={dp}_{{x}} {dp}_{{y}\:} {dp}_{{z}} \:\:{then} \\ $$$${find} \\ $$$$\:\int_{\mathrm{0}} ^{\infty} \:{P}^{\mathrm{2}\:} {e}^{\frac{{p}^{\mathrm{2}} }{\mathrm{2}{mKT}\:}} \:\:{d}^{\mathrm{3}} {p}\:\:=.... \\ $$$$ \\ $$$$ \\ $$

Question Number 158693 Answers: 1 Comments: 0

Question Number 158596 Answers: 1 Comments: 0

calculate : Ω = ∫_0 ^( (π/4)) (( 1+ tan^( 4) (x))/(cot^( 2) (x))) dx=?

$$ \\ $$$$\:\:\:\:\:{calculate}\:: \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\mathrm{1}+\:{tan}^{\:\mathrm{4}} \left({x}\right)}{{cot}^{\:\mathrm{2}} \left({x}\right)}\:{dx}=? \\ $$$$ \\ $$

Question Number 158593 Answers: 1 Comments: 0

Question Number 158591 Answers: 0 Comments: 2

I=∫ (dx/(1+x^6 )) =?

$$\:{I}=\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} }\:=? \\ $$

Question Number 158586 Answers: 0 Comments: 5

Question Number 158567 Answers: 0 Comments: 2

show that (√3) is an irrarional number

$$\:\mathrm{show}\:\mathrm{that}\:\sqrt{\mathrm{3}}\:\mathrm{is}\:\mathrm{an}\: \\ $$$$\:\mathrm{irrarional}\:\mathrm{number} \\ $$

Question Number 158561 Answers: 0 Comments: 2

Question Number 159045 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (1/((3n+1)^3 ))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$

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