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AllQuestion and Answers: Page 1235

Question Number 91230 Answers: 2 Comments: 0

Σ_(j=o) ^m ^a C_j ^b C_(m−j) = ^(a+b) C_m solve this problem

$$\underset{{j}={o}} {\overset{{m}} {\sum}}\:\:\overset{{a}} {\:}{C}_{{j}} \:\overset{{b}} {\:}{C}_{{m}−{j}} \:\:=\:\overset{{a}+{b}} {\:}{C}_{{m}} \\ $$$${solve}\:{this}\:{problem} \\ $$

Question Number 91228 Answers: 0 Comments: 1

lim_(x→1) lnx(∫_0 ^x (dt/(lnt)) )

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:{lnx}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{dt}}{{lnt}}\:\right)\: \\ $$

Question Number 91223 Answers: 1 Comments: 0

what is complementary error function erfc(t)?

$${what}\:{is}\:{complementary}\:{error}\:{function} \\ $$$${erfc}\left({t}\right)? \\ $$

Question Number 91220 Answers: 0 Comments: 3

∫_1 ^x ((lnt)/(1+t^2 ))dt

$$\int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{lnt}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\mathrm{dt} \\ $$

Question Number 91217 Answers: 0 Comments: 3

Question Number 91211 Answers: 1 Comments: 1

x dy +5y dx = 2y^4 x dx

$${x}\:{dy}\:+\mathrm{5}{y}\:{dx}\:=\:\mathrm{2}{y}^{\mathrm{4}} {x}\:{dx} \\ $$

Question Number 91196 Answers: 1 Comments: 1

Question Number 91195 Answers: 1 Comments: 0

what is the duble fictorial furmolla?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{duble}\:\mathrm{fictorial}\:\mathrm{furmolla}? \\ $$

Question Number 91185 Answers: 1 Comments: 2

f(x)=(x−3)^5 ln(1+x) f^((2020)) (3)=?

$${f}\left({x}\right)=\left({x}−\mathrm{3}\right)^{\mathrm{5}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$${f}^{\left(\mathrm{2020}\right)} \left(\mathrm{3}\right)=? \\ $$

Question Number 91183 Answers: 0 Comments: 0

Question Number 91182 Answers: 1 Comments: 0

lim_(x→0) ((2x^6 +3x^2 −3tan^2 x)/(3x^6 ))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}^{\mathrm{6}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3tan}\:^{\mathrm{2}} {x}}{\mathrm{3}{x}^{\mathrm{6}} } \\ $$

Question Number 91178 Answers: 0 Comments: 2

Question Number 91176 Answers: 0 Comments: 1

My Post Filter Issue Dear Mr W, can you send a few screenshots on what is seen when using filter myposts. Thank You

$$\mathrm{My}\:\mathrm{Post}\:\mathrm{Filter}\:\mathrm{Issue} \\ $$$$\mathrm{Dear}\:\mathrm{Mr}\:\mathrm{W},\:\mathrm{can}\:\mathrm{you}\:\mathrm{send}\:\mathrm{a}\:\mathrm{few}\:\mathrm{screenshots} \\ $$$$\mathrm{on}\:\mathrm{what}\:\mathrm{is}\:\mathrm{seen}\:\mathrm{when}\:\mathrm{using}\:\mathrm{filter} \\ $$$$\mathrm{myposts}.\:\mathrm{Thank}\:\mathrm{You} \\ $$

Question Number 91177 Answers: 1 Comments: 1

6^((log_2 x)^2 ) + x^((log_2 x)) = 12

$$\mathrm{6}^{\left(\mathrm{log}_{\mathrm{2}} \:{x}\right)^{\mathrm{2}} } \:+\:{x}^{\left(\mathrm{log}_{\mathrm{2}} \:{x}\right)} \:=\:\mathrm{12}\: \\ $$

Question Number 91167 Answers: 1 Comments: 4

Question Number 91166 Answers: 0 Comments: 7

Question Number 91158 Answers: 0 Comments: 3

lim_(x→∞) (√(4x^2 +2x)) − ((8x^3 +4x^2 ))^(1/(3 ))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}}\:−\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{8}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} } \\ $$

Question Number 91157 Answers: 0 Comments: 1

lim_(x→0) ((3tan 4x−4tan 3x)/(3sin 4x−4sin 3x)) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4}{x}−\mathrm{4tan}\:\mathrm{3}{x}}{\mathrm{3sin}\:\mathrm{4}{x}−\mathrm{4sin}\:\mathrm{3}{x}}\:=\:? \\ $$

Question Number 91154 Answers: 1 Comments: 1

lim_(x→0) ((12−6x^2 −12cos x)/x^4 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{12}−\mathrm{6}{x}^{\mathrm{2}} −\mathrm{12cos}\:{x}}{{x}^{\mathrm{4}} } \\ $$

Question Number 91147 Answers: 2 Comments: 1

(D^2 +1)^2 y = x^2 cos x

$$\left({D}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} {y}\:=\:{x}^{\mathrm{2}} \mathrm{cos}\:{x}\: \\ $$

Question Number 91139 Answers: 0 Comments: 1

(dy/dx) = ((y−x+1)/(y−x+5))

$$\frac{{dy}}{{dx}}\:=\:\frac{{y}−{x}+\mathrm{1}}{{y}−{x}+\mathrm{5}} \\ $$

Question Number 91149 Answers: 1 Comments: 1

A particle starts from rest and moves in a straight line on a smooth horizontal surface. Its acceleration at time t seconds is given by k(4v + 1) ms^(−2) where k is a positve constant and v ms^(−1) is the speed of the particle. Given that v = ((e^2 −1)/4) when t = 1. show that v = (1/4)(e^(2t) −1)

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\: \\ $$$$\mathrm{horizontal}\:\mathrm{surface}.\:\mathrm{Its}\:\mathrm{acceleration}\:\mathrm{at}\:\mathrm{time}\:{t}\:\mathrm{seconds}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{k}\left(\mathrm{4}{v}\:+\:\mathrm{1}\right)\:\mathrm{ms}^{−\mathrm{2}} \\ $$$$\mathrm{where}\:{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positve}\:\mathrm{constant}\:\mathrm{and}\:{v}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}. \\ $$$$\mathrm{Given}\:\mathrm{that}\:{v}\:=\:\frac{{e}^{\mathrm{2}} −\mathrm{1}}{\mathrm{4}}\:\mathrm{when}\:{t}\:=\:\mathrm{1}.\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{v}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\left({e}^{\mathrm{2}{t}} −\mathrm{1}\right) \\ $$

Question Number 91133 Answers: 1 Comments: 2

lim_(x→1) (((x−1)+((1−x))^(1/(3 )) )/((1−x^2 ))^(1/(3 )) ) =

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\left({x}−\mathrm{1}\right)+\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}−{x}}}{\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\: \\ $$

Question Number 91119 Answers: 0 Comments: 0

∫_0 ^( ∫_0 ^( k) (1 + (1/x))^x dx) sin (x^e ) dx = (π/e) k = ?

$$\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\int_{\mathrm{0}} ^{\:{k}} \:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)^{{x}} {dx}} \:\mathrm{sin}\:\left({x}^{{e}} \right)\:{dx}\:=\:\frac{\pi}{{e}} \\ $$$$\:{k}\:=\:? \\ $$

Question Number 91099 Answers: 1 Comments: 12

Question Number 91088 Answers: 0 Comments: 0

let U_n =∫_0 ^(1/2) (dx/(√(1−x^n ))) calculate lim_(n→+∞) U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{dx}}{\sqrt{\mathrm{1}−{x}^{{n}} }}\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$

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