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Question Number 83621 Answers: 2 Comments: 1

∣ x+(1/x)∣ < 4 find the solution

$$\mid\:{x}+\frac{\mathrm{1}}{{x}}\mid\:<\:\mathrm{4}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 83524 Answers: 2 Comments: 2

Question Number 83521 Answers: 0 Comments: 1

∫((√(sin(x)))/(sin^2 (x)+1)) dx

$$\int\frac{\sqrt{{sin}\left({x}\right)}}{{sin}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}\:{dx} \\ $$

Question Number 83520 Answers: 1 Comments: 0

closest distance point (6,9) to curve y = x^2 −12x+32 . mister w your method can be applied to this problem?

$$\mathrm{closest}\:\mathrm{distance}\:\mathrm{point}\:\left(\mathrm{6},\mathrm{9}\right)\: \\ $$$$\mathrm{to}\:\mathrm{curve}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{12x}+\mathrm{32}\:. \\ $$$$\mathrm{mister}\:\mathrm{w}\:\mathrm{your}\:\mathrm{method}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{applied}\:\mathrm{to}\:\mathrm{this}\:\mathrm{problem}? \\ $$

Question Number 83513 Answers: 0 Comments: 2

If m tan (θ−30^o ) = n tan (θ+12^o ) prove that cos 2θ = ((m+n)/(2(m−n)))

$$\mathrm{If}\:\mathrm{m}\:\mathrm{tan}\:\left(\theta−\mathrm{30}^{\mathrm{o}} \right)\:=\:\mathrm{n}\:\mathrm{tan}\:\left(\theta+\mathrm{12}^{\mathrm{o}} \right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{cos}\:\mathrm{2}\theta\:=\:\frac{\mathrm{m}+\mathrm{n}}{\mathrm{2}\left(\mathrm{m}−\mathrm{n}\right)} \\ $$

Question Number 83512 Answers: 1 Comments: 0

find the solution ((4x^2 )/((1−(√(2x+1)))^2 )) < 2x+9

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\left(\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{1}}\right)^{\mathrm{2}} }\:<\:\mathrm{2x}+\mathrm{9} \\ $$

Question Number 83511 Answers: 1 Comments: 0

find minimum value of ∣x−y∣ +(√((x−3)^2 +(y+1)^2 ))

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mid\mathrm{x}−\mathrm{y}\mid\:+\sqrt{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 83500 Answers: 1 Comments: 0

(d/dx)((a+bx)^(c+dx) )

$$\frac{{d}}{{dx}}\left(\left({a}+{bx}\right)^{{c}+{dx}} \right) \\ $$

Question Number 83495 Answers: 0 Comments: 5

closest distance point (3,0) to curve y^2 = x+4 ?

$$\mathrm{closest}\:\mathrm{distance}\:\mathrm{point}\:\left(\mathrm{3},\mathrm{0}\right)\:\mathrm{to}\:\mathrm{curve}\: \\ $$$$\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{x}+\mathrm{4}\:? \\ $$

Question Number 83493 Answers: 0 Comments: 0

If lim_(x→p) ((∣x+p∣^2 −∣2p∣^2 )/(p^2 −x^2 )) = L find lim_(x→p) ((∣2p∣^3 −∣x+p∣^3 )/(x−p))

$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{2}} −\mid\mathrm{2p}\mid^{\mathrm{2}} }{\mathrm{p}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{L} \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{2p}\mid^{\mathrm{3}} −\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{3}} }{\mathrm{x}−\mathrm{p}} \\ $$

Question Number 83488 Answers: 1 Comments: 0

∫ ((x^3 −1)/(√(x^2 −1))) dx = ?

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 83481 Answers: 1 Comments: 3

Question Number 83477 Answers: 0 Comments: 1

a^b +b^a =1 a=? , b=? a≠b≠0

$${a}^{{b}} +{b}^{{a}} =\mathrm{1}\:\:\:{a}=?\:,\:{b}=? \\ $$$${a}\neq{b}\neq\mathrm{0} \\ $$

Question Number 83473 Answers: 1 Comments: 0

solve in R sin(πln(x))+cos(πln(x))=1

$${solve}\:{in}\:{R} \\ $$$${sin}\left(\pi{ln}\left({x}\right)\right)+{cos}\left(\pi{ln}\left({x}\right)\right)=\mathrm{1} \\ $$

Question Number 83471 Answers: 2 Comments: 1

Question Number 83459 Answers: 0 Comments: 2

Question Number 83445 Answers: 2 Comments: 1

The nearest distance of (0, 3) to curve : y = 6 − x^2 is ...

$${The}\:\:{nearest}\:\:{distance}\:\:{of}\:\:\left(\mathrm{0},\:\mathrm{3}\right)\:\:{to}\:\:{curve}\:\::\:\:{y}\:=\:\:\mathrm{6}\:−\:{x}^{\mathrm{2}} \:\:{is}\:\:... \\ $$

Question Number 83441 Answers: 1 Comments: 0

calculate ∫_0 ^(π/4) (√(1+2tanx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{\mathrm{1}+\mathrm{2}{tanx}}{dx} \\ $$

Question Number 83440 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (dx/(sinx^(cosx) +cosx^(sinx) ))

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{sinx}^{{cosx}} +{cosx}^{{sinx}} } \\ $$

Question Number 83430 Answers: 1 Comments: 0

prove that? sin 3θ sin^3 θ + cos 3θ cos^3 θ = cos^3 (2θ)

$$\mathrm{prove}\:\mathrm{that}? \\ $$$$\mathrm{sin}\:\mathrm{3}\theta\:\mathrm{sin}^{\mathrm{3}} \:\theta\:+\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:^{\mathrm{3}} \theta\:=\:\: \\ $$$$\mathrm{cos}\:^{\mathrm{3}} \:\left(\mathrm{2}\theta\right) \\ $$

Question Number 83425 Answers: 0 Comments: 1

((tan 3a)/(tan a)) = k show that ((sin 3a)/(sin a)) = ((2k)/(k−1))

$$\frac{\mathrm{tan}\:\mathrm{3a}}{\mathrm{tan}\:\mathrm{a}}\:=\:\mathrm{k} \\ $$$$\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{sin}\:\mathrm{3a}}{\mathrm{sin}\:\mathrm{a}}\:=\:\frac{\mathrm{2k}}{\mathrm{k}−\mathrm{1}} \\ $$

Question Number 83492 Answers: 0 Comments: 0

f(x)= (1/(2(√x))) lim_(t→0) ((f(2x−t)+f(2x−2t)−2f(2x+t))/t)

$$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{2x}−\mathrm{t}\right)+\mathrm{f}\left(\mathrm{2x}−\mathrm{2t}\right)−\mathrm{2f}\left(\mathrm{2x}+\mathrm{t}\right)}{\mathrm{t}} \\ $$

Question Number 83491 Answers: 0 Comments: 1

f(x) = (((√(1+sin (2x)))−(√(1−2sin (x))))/x) g(x) = 2x+(√(2x)) find lim_(x→0) g(f(x))

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\sqrt{\mathrm{1}+\mathrm{sin}\:\left(\mathrm{2x}\right)}−\sqrt{\mathrm{1}−\mathrm{2sin}\:\left(\mathrm{x}\right)}}{\mathrm{x}} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\sqrt{\mathrm{2x}} \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\: \\ $$

Question Number 83420 Answers: 1 Comments: 4

find range x of function x−4(√y) = 2(√(x−y))

$$\mathrm{find}\:\mathrm{range}\:\mathrm{x}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{x}−\mathrm{4}\sqrt{\mathrm{y}}\:=\:\mathrm{2}\sqrt{\mathrm{x}−\mathrm{y}} \\ $$

Question Number 83413 Answers: 1 Comments: 3

y = x ∣x∣ find y ′ ?

$$\mathrm{y}\:=\:\mathrm{x}\:\mid\mathrm{x}\mid \\ $$$$\mathrm{find}\:\mathrm{y}\:'\:? \\ $$

Question Number 83411 Answers: 2 Comments: 1

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