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Question Number 83603 Answers: 0 Comments: 4

∫ (dx/(1−2cos x))

$$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{x}} \\ $$

Question Number 83599 Answers: 0 Comments: 0

Question Number 83597 Answers: 0 Comments: 1

∫_0 ^2 (3x^2 −4x+2)dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\right){dx} \\ $$

Question Number 83591 Answers: 0 Comments: 1

3x^2 −x+(t^2 −4t+3) = 0 has a roots sin α and cos α. find (√(t^2 −4t+5))

$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}+\left(\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{3}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{roots}\:\mathrm{sin}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\alpha. \\ $$$$\mathrm{find}\:\sqrt{\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{5}} \\ $$

Question Number 83590 Answers: 0 Comments: 3

transform the ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 to the polar equation r= ((a(1−e^2 ))/(1+ecosθ)) a: semimajor axis e: eccentricity

$${transform}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{to} \\ $$$${the}\:{polar}\:{equation}\:{r}=\:\frac{{a}\left(\mathrm{1}−{e}^{\mathrm{2}} \right)}{\mathrm{1}+{ecos}\theta} \\ $$$${a}:\:{semimajor}\:{axis} \\ $$$${e}:\:{eccentricity} \\ $$

Question Number 83587 Answers: 0 Comments: 2

lim_(x→0) ((3sin πx−sin 3πx)/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3sin}\:\pi\mathrm{x}−\mathrm{sin}\:\mathrm{3}\pi\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 83582 Answers: 0 Comments: 0

Given A = 580^o find sin ((A/2)) in term sin (A)

$$\mathrm{Given}\:\mathrm{A}\:=\:\mathrm{580}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\mathrm{sin}\:\left(\frac{\mathrm{A}}{\mathrm{2}}\right)\:\mathrm{in}\:\mathrm{term}\:\mathrm{sin}\:\left(\mathrm{A}\right) \\ $$

Question Number 83570 Answers: 2 Comments: 3

Find the locus of a point which moves such that its distance from the line y = 4 is a constant k.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{4}\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\:\:\mathrm{k}. \\ $$

Question Number 83569 Answers: 0 Comments: 1

calculate ∫_1 ^(+∞) (dx/(x^4 (3x−1)^5 ))

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 83565 Answers: 1 Comments: 4

Question Number 83559 Answers: 1 Comments: 1

Question Number 83558 Answers: 0 Comments: 4

Question Number 83556 Answers: 2 Comments: 0

find the value of (b) wich makes the line y=b divide the tow funtions into tow equal parts 1) f(x)=9−x^2 , g(x)=0 2)f(x)=9−∣x∣ , g(x)=0

$${find}\:{the}\:{value}\:{of}\:\:\left({b}\right)\:{wich}\:{makes}\:{the} \\ $$$${line}\:{y}={b}\:{divide}\:{the}\:{tow}\:{funtions}\:{into} \\ $$$${tow}\:{equal}\:{parts} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x}\right)=\mathrm{9}−{x}^{\mathrm{2}} \:,\:{g}\left({x}\right)=\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){f}\left({x}\right)=\mathrm{9}−\mid{x}\mid\:,\:{g}\left({x}\right)=\mathrm{0} \\ $$

Question Number 83554 Answers: 1 Comments: 0

Question Number 83543 Answers: 1 Comments: 2

Question Number 83542 Answers: 2 Comments: 0

Question Number 83539 Answers: 0 Comments: 3

what is range of function f(x) = (x/(√(x^2 −1)))?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}? \\ $$

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 ?

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

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