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Question Number 178743 Answers: 0 Comments: 2

f(x)=arctan((√((x−1)/(2x+1)))) f^(−1) (x)=?

$${f}\left({x}\right)={arctan}\left(\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}}\right)\:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 178737 Answers: 2 Comments: 0

Question Number 178932 Answers: 1 Comments: 0

Question Number 178725 Answers: 0 Comments: 0

Let a be a positive number. Then (√a)=(√((−a)(−1)))=(√(−a))∙i=(√(a(−1)))∙i=(√a)∙i^2 =−(√a) Where is the mistake?

$$\mathrm{Let}\:{a}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{number}.\:\mathrm{Then} \\ $$$$\sqrt{{a}}=\sqrt{\left(−{a}\right)\left(−\mathrm{1}\right)}=\sqrt{−{a}}\centerdot{i}=\sqrt{{a}\left(−\mathrm{1}\right)}\centerdot{i}=\sqrt{{a}}\centerdot{i}^{\mathrm{2}} =−\sqrt{{a}} \\ $$$$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}? \\ $$

Question Number 178716 Answers: 2 Comments: 0

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

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

Question Number 178715 Answers: 0 Comments: 0

The solution of 2≤ax^2 +bx+c≤3 is [2, 3] 1) if a>0, ax^2 +(b−3)x−c≤0 has and only has 10 integer solutions. find the range of a. 2) find x: ax^2 +(b−1)x+5<0

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{2}\leqslant{ax}^{\mathrm{2}} +{bx}+{c}\leqslant\mathrm{3}\:\mathrm{is}\:\left[\mathrm{2},\:\mathrm{3}\right] \\ $$$$\left.\mathrm{1}\right)\:\mathrm{if}\:{a}>\mathrm{0},\:{ax}^{\mathrm{2}} +\left({b}−\mathrm{3}\right){x}−{c}\leqslant\mathrm{0}\:\mathrm{has}\:\mathrm{and}\:\mathrm{only}\:\mathrm{has}\:\mathrm{10}\:\mathrm{integer}\:\mathrm{solutions}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:{x}:\:{ax}^{\mathrm{2}} +\left({b}−\mathrm{1}\right){x}+\mathrm{5}<\mathrm{0} \\ $$

Question Number 178712 Answers: 1 Comments: 0

Question Number 178697 Answers: 1 Comments: 3

Question Number 178694 Answers: 1 Comments: 0

Find the general solution of 2^(cos 2θ) +1=3.2^(−sin^2 θ)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{2}^{\mathrm{cos}\:\mathrm{2}\theta} +\mathrm{1}=\mathrm{3}.\mathrm{2}^{−\mathrm{sin}\:^{\mathrm{2}} \theta} \\ $$

Question Number 178693 Answers: 1 Comments: 6

Prove that ∫_0 ^(π/2) ((tan 2x)/( (√(sin^4 x+4cos^2 x)) −(√(cos^4 x+4sin^2 x))))=1

$$\mathrm{P}{rove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{tan}\:\mathrm{2x}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}}\:−\sqrt{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}}=\mathrm{1} \\ $$

Question Number 178692 Answers: 1 Comments: 0

∫((tan (ln x).tan (ln (x/2)).tan (ln 2))/x)dx

$$\int\frac{\mathrm{tan}\:\left(\mathrm{ln}\:{x}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\frac{{x}}{\mathrm{2}}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\mathrm{2}\right)}{{x}}{dx} \\ $$$$ \\ $$

Question Number 178682 Answers: 0 Comments: 0

Corona virus (covid −19) is spreading through a certain country. Let the constant S be the number of people susceptible to infection. The infection rate is proportional to the the product of the already infected people (x) and the number of susceptible but but uninfected people (S−x). establish the differential equation.

$$\mathrm{Corona}\:\mathrm{virus}\:\left(\mathrm{covid}\:−\mathrm{19}\right)\:\mathrm{is}\:\mathrm{spreading}\:\mathrm{through}\:\mathrm{a} \\ $$$$\mathrm{certain}\:\mathrm{country}.\:\mathrm{Let}\:\mathrm{the}\:\mathrm{constant}\:{S}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{people}\:\mathrm{susceptible}\:\mathrm{to}\:\mathrm{infection}.\:\:\mathrm{The}\:\mathrm{infection}\:\mathrm{rate} \\ $$$$\mathrm{is}\:\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{already} \\ $$$$\mathrm{infected}\:\mathrm{people}\:\left({x}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{susceptible}\:\mathrm{but}\: \\ $$$$\mathrm{but}\:\mathrm{uninfected}\:\mathrm{people}\:\left({S}−{x}\right).\:\mathrm{establish}\:\mathrm{the}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}. \\ $$

Question Number 178678 Answers: 0 Comments: 0

Cacul lim_(n→+∝) n[(e^(−2(√n)) /e^(−2(√(n+1))) ) −1]=....

$${Cacul} \\ $$$${li}\underset{{n}\rightarrow+\propto} {{m}}\:\:\:\:{n}\left[\frac{{e}^{−\mathrm{2}\sqrt{{n}}} }{{e}^{−\mathrm{2}\sqrt{{n}+\mathrm{1}}} }\:−\mathrm{1}\right]=.... \\ $$

Question Number 178673 Answers: 2 Comments: 0