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Question Number 109913 Answers: 1 Comments: 0

((16))^(1/(x−1)) −5 (4)^(1/(x−1)) +2=0 find x?

$$\sqrt[{{x}−\mathrm{1}}]{\mathrm{16}}−\mathrm{5}\:\:\sqrt[{{x}−\mathrm{1}}]{\mathrm{4}}+\mathrm{2}=\mathrm{0}\:{find}\:{x}? \\ $$

Question Number 109912 Answers: 2 Comments: 1

(1)∫∣((x+3)/(x+1))∣dx (2)∫x∣x−1∣dx (3)∫e^((x−1)/x) dx

$$\left(\mathrm{1}\right)\int\mid\frac{{x}+\mathrm{3}}{{x}+\mathrm{1}}\mid{dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int{x}\mid{x}−\mathrm{1}\mid{dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int{e}^{\frac{{x}−\mathrm{1}}{{x}}} {dx} \\ $$

Question Number 110178 Answers: 1 Comments: 0

Define the laplace transformation equation and use the transformation equation transform (dy/dx) and (d^2 y/dx^2 ) hence solve the equation : (d^2 y/dx^2 ) + 5 (dy/dx) + 4 = e^(−x) sin 2x Using the laplace transformation equations derived above.

$$\mathrm{Define}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{transformation}\:\mathrm{equation}\:\mathrm{and} \\ $$$$\mathrm{use}\:\mathrm{the}\:\mathrm{transformation}\:\mathrm{equation}\:\mathrm{transform}\:\frac{{dy}}{{dx}}\:\mathrm{and}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} } \\ $$$$\mathrm{hence}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\::\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{5}\:\frac{{dy}}{{dx}}\:+\:\mathrm{4}\:=\:{e}^{−{x}} \:\mathrm{sin}\:\mathrm{2}{x} \\ $$$$\mathrm{Using}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{transformation}\:\mathrm{equations}\:\mathrm{derived}\:\mathrm{above}. \\ $$

Question Number 109910 Answers: 0 Comments: 2

Question Number 109909 Answers: 2 Comments: 6

Question Number 109905 Answers: 1 Comments: 0

Question Number 109901 Answers: 1 Comments: 0

If first n terms of an A.P. is cn^2 , find sum of squares of its first n terms.

$${If}\:{first}\:{n}\:{terms}\:{of}\:{an}\:{A}.{P}.\:{is}\:{cn}^{\mathrm{2}} , \\ $$$${find}\:{sum}\:{of}\:{squares}\:{of}\:{its}\:{first} \\ $$$${n}\:{terms}. \\ $$

Question Number 109895 Answers: 1 Comments: 3

Question Number 109891 Answers: 1 Comments: 0

((Δbe▽)/(math)) ∫ ((arc tan x)/((1+(1/x^2 )))) dx ?

$$\:\:\frac{\Delta{be}\bigtriangledown}{{math}} \\ $$$$\int\:\frac{\mathrm{arc}\:\mathrm{tan}\:{x}}{\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}\:{dx}\:? \\ $$

Question Number 109888 Answers: 3 Comments: 0

2^(x+5) =(√8^x )

$$\mathrm{2}^{{x}+\mathrm{5}} =\sqrt{\mathrm{8}^{{x}} } \\ $$

Question Number 109884 Answers: 1 Comments: 1

Question Number 109872 Answers: 2 Comments: 1

((★be★)/(Math)) ∫ ((cos x dx)/(sin^2 x+4sin x−5)) ?

$$\:\:\frac{\bigstar{be}\bigstar}{\mathcal{M}{ath}} \\ $$$$\int\:\frac{\mathrm{cos}\:{x}\:{dx}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{4sin}\:{x}−\mathrm{5}}\:? \\ $$

Question Number 109863 Answers: 1 Comments: 0

Question Number 109861 Answers: 3 Comments: 0

((JS)/(■★★■)) lim_(x→3) ((5−2x+(√(x−2)))/(x−4+(√(x−2)))) ?

$$\:\:\frac{{JS}}{\blacksquare\bigstar\bigstar\blacksquare} \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{5}−\mathrm{2}{x}+\sqrt{{x}−\mathrm{2}}}{{x}−\mathrm{4}+\sqrt{{x}−\mathrm{2}}}\:? \\ $$

Question Number 109858 Answers: 3 Comments: 0

Find the nth term for the sequence 3. 12. 27. 48. 75...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{for}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{3}.\:\mathrm{12}.\:\mathrm{27}.\:\mathrm{48}.\:\mathrm{75}... \\ $$

Question Number 109855 Answers: 3 Comments: 0

Question Number 109854 Answers: 4 Comments: 1

((★be★)/(math)) (1)∫ ((3+2cos x)/((2+3cos x)^3 )) dx (2)((√(2+(√3))) )^y −((√(2−(√3))) )^y = 14 y=?

$$\:\frac{\bigstar{be}\bigstar}{{math}} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{3}+\mathrm{2cos}\:{x}}{\left(\mathrm{2}+\mathrm{3cos}\:{x}\right)^{\mathrm{3}} }\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:\right)^{{y}} −\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:\right)^{{y}} \:=\:\mathrm{14} \\ $$$$\:\:\:\:\:{y}=? \\ $$

Question Number 109853 Answers: 0 Comments: 2

is there any diffrence between greatest coefficient and largest coefficient?

$${is}\:{there}\:{any}\:{diffrence}\:{between}\:{greatest} \\ $$$${coefficient}\:{and}\:{largest}\:{coefficient}? \\ $$

Question Number 109849 Answers: 0 Comments: 0

Question Number 109852 Answers: 0 Comments: 1

pls is there anyone with any material that can help me for binomial expansion for negative powers

$${pls}\:{is}\:{there}\:{anyone}\:{with}\:{any}\:{material}\:{that} \\ $$$${can}\:{help}\:{me}\:{for}\:{binomial}\:{expansion}\:{for} \\ $$$${negative}\:{powers} \\ $$

Question Number 109839 Answers: 4 Comments: 1

((JS)/(≈♥≈)) (1) ∫ (((√(x+1))−(√(x−1)))/( (√(x+1))+(√(x−1)))) dx (2) ∫ ((√(tan x))/(1+(√(tan x)) )) dx

$$\:\frac{{JS}}{\approx\heartsuit\approx} \\ $$$$\left(\mathrm{1}\right)\:\int\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\sqrt{\mathrm{tan}\:{x}}\:}\:{dx}\: \\ $$

Question Number 109838 Answers: 1 Comments: 0

please prove::: ∫_0 ^( 1) (1/( (√(1−x))))log((x/(1−x)))dx =4log(2)

$$ \\ $$$$ \\ $$$$\:\:\:\:{please}\:{prove}::: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}}}{log}\left(\frac{{x}}{\mathrm{1}−{x}}\right){dx}\:=\mathrm{4}{log}\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 109834 Answers: 3 Comments: 1

Question Number 109823 Answers: 1 Comments: 1

Question Number 109820 Answers: 0 Comments: 2

tan^2 x+tan^2 2x+tan^2 4x=33 find x (show full solution please)

$${tan}^{\mathrm{2}} {x}+{tan}^{\mathrm{2}} \mathrm{2}{x}+{tan}^{\mathrm{2}} \mathrm{4}{x}=\mathrm{33} \\ $$$${find}\:{x}\:\:\:\left({show}\:{full}\:{solution}\:{please}\right) \\ $$

Question Number 109818 Answers: 1 Comments: 7

tanx+tan2x=1 find the general solution

$${tanx}+{tan}\mathrm{2}{x}=\mathrm{1} \\ $$$${find}\:{the}\:{general}\:{solution} \\ $$

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