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AllQuestion and Answers: Page 1317

Question Number 81771 Answers: 1 Comments: 3

Question Number 81769 Answers: 0 Comments: 2

Question Number 81768 Answers: 1 Comments: 4

Question Number 81763 Answers: 0 Comments: 2

Q. Find the minimum value of 3cosx + 4sinx + 8.

$${Q}.\:{Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{3}{cosx}\:+\:\mathrm{4}{sinx}\:+\:\mathrm{8}. \\ $$

Question Number 81760 Answers: 0 Comments: 2

prove sin a+sin b+sin c =? 4cos ((a/2))cos ((b/2))cos ((c/2))

$${prove}\: \\ $$$$\mathrm{sin}\:{a}+\mathrm{sin}\:{b}+\mathrm{sin}\:{c}\:=? \\ $$$$\mathrm{4cos}\:\left(\frac{{a}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{b}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{c}}{\mathrm{2}}\right) \\ $$

Question Number 81759 Answers: 0 Comments: 1

Question Number 81755 Answers: 1 Comments: 0

Question Number 81750 Answers: 0 Comments: 0

Question Number 81741 Answers: 0 Comments: 2

Question Number 81740 Answers: 0 Comments: 1

Question Number 81739 Answers: 2 Comments: 1

∫(dx/(cos^3 x−sin^3 x))

$$\int\frac{{dx}}{{cos}^{\mathrm{3}} {x}−{sin}^{\mathrm{3}} {x}} \\ $$

Question Number 81734 Answers: 0 Comments: 4

The vertices of quadrilateral lie on the graph of y = lnx and the x−coordinates of these vertices are consecutive positive integer . The area of the quadrilateral is ln (((91)/(90))). what is the x−coordinate of the leftmost vertex

$${The}\:{vertices}\:{of}\:{quadrilateral} \\ $$$${lie}\:{on}\:{the}\:{graph}\:{of}\:{y}\:=\:{lnx}\:{and}\: \\ $$$${the}\:{x}−{coordinates}\:{of}\:{these}\:{vertices} \\ $$$${are}\:{consecutive}\:{positive}\:{integer} \\ $$$$.\:{The}\:{area}\:{of}\:{the}\:{quadrilateral} \\ $$$${is}\:{ln}\:\left(\frac{\mathrm{91}}{\mathrm{90}}\right).\:{what}\:{is}\:{the}\:{x}−{coordinate} \\ $$$${of}\:{the}\:{leftmost}\:{vertex} \\ $$

Question Number 81733 Answers: 0 Comments: 2

Σ_(n=1) ^∞ (n/((n+1)∙5^n )) = ?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}}{\left({n}+\mathrm{1}\right)\centerdot\mathrm{5}^{{n}} }\:\:=\:\:? \\ $$

Question Number 81731 Answers: 0 Comments: 1

If a, b, c are in AP; p, q, r are in HP and ap, bq, cr are in GP, then (p/r)+(r/p) is equal to

$$\mathrm{If}\:\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP};\:\:{p},\:{q},\:{r}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP}\: \\ $$$$\mathrm{and}\:\:{ap},\:{bq},\:{cr}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP},\:\mathrm{then}\:\frac{{p}}{{r}}+\frac{{r}}{{p}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 81725 Answers: 0 Comments: 1

If 7 points out of 12 are in the same straight line, then the number of triangles formed is

$$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$

Question Number 81724 Answers: 0 Comments: 2

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{an} \\ $$$$\mathrm{examiner}\:\mathrm{can}\:\mathrm{assign}\:\mathrm{30}\:\mathrm{marks}\:\mathrm{to}\:\mathrm{8} \\ $$$$\mathrm{questions},\:\mathrm{giving}\:\mathrm{not}\:\mathrm{less}\:\mathrm{than}\:\mathrm{2}\:\mathrm{marks} \\ $$$$\mathrm{to}\:\mathrm{any}\:\mathrm{question}\:\mathrm{is} \\ $$

Question Number 81704 Answers: 0 Comments: 0

find Γ((1/3)) and Γ((2/3))

$${find}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:{and}\:\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right) \\ $$

Question Number 81698 Answers: 1 Comments: 1

Question Number 81692 Answers: 0 Comments: 1

Question Number 81684 Answers: 1 Comments: 1

∫ (dx/(x^3 + 1)) = ...

$$\int\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\:=\:\:... \\ $$

Question Number 81720 Answers: 0 Comments: 2

let f(x)=arctan(1+x^2 ) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developpf at integr serie

$${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developpf}\:{at}\:{integr}\:{serie} \\ $$

Question Number 81719 Answers: 0 Comments: 1

1) find ∫ (dx/((x+2)^5 (x−3)^9 )) 2) calculate ∫_4 ^(+∞) (dx/((x+2)^5 (x−3)^9 ))

$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$

Question Number 81674 Answers: 2 Comments: 3

Question Number 81672 Answers: 0 Comments: 3

If x ∈ R, the least value of the expression ((x^2 −6x+5)/(x^2 +2x+1)) is

$$\mathrm{If}\:{x}\:\in\:{R},\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expression}\:\frac{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}\:\mathrm{is} \\ $$

Question Number 81664 Answers: 0 Comments: 4

∫_(−π/4) ^(π/4) e^(−x) sin x dx =

$$\underset{−\pi/\mathrm{4}} {\overset{\pi/\mathrm{4}} {\int}}\:{e}^{−{x}} \:\mathrm{sin}\:{x}\:{dx}\:= \\ $$

Question Number 81663 Answers: 0 Comments: 2

∫_( 0) ^1 x (1−x)^n dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:{x}\:\left(\mathrm{1}−{x}\right)^{{n}} \:{dx}\:= \\ $$

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