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Question Number 91479 Answers: 1 Comments: 4

∫_(−π/2 ) ^(π/2) (√(cos x−cos^3 x)) dx=...

$$\:\underset{−\pi/\mathrm{2}\:} {\overset{\pi/\mathrm{2}} {\int}}\:\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}^{\mathrm{3}} {x}}\:\mathrm{dx}=... \\ $$

Question Number 91476 Answers: 0 Comments: 2

Find the slope of the tangent line to the graph of: y^4 +3y−4x^3 =5x+1 at the point P (1, −2)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{line}\:\mathrm{to}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}: \\ $$$$\mathrm{y}^{\mathrm{4}} +\mathrm{3y}−\mathrm{4x}^{\mathrm{3}} =\mathrm{5x}+\mathrm{1}\:\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{P}\:\left(\mathrm{1},\:−\mathrm{2}\right) \\ $$

Question Number 91474 Answers: 0 Comments: 0

f(x)=(√(4−x^2 )) and g(x)=3x+1 find the sum , different, and product f(x) and g(x).

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:,\:\mathrm{different},\:\mathrm{and}\:\mathrm{product} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 91473 Answers: 1 Comments: 0

Question Number 91471 Answers: 1 Comments: 0

∣2x−7∣>3

$$\mid\mathrm{2x}−\mathrm{7}\mid>\mathrm{3} \\ $$

Question Number 91470 Answers: 0 Comments: 2

∣x−3∣<0.1

$$\mid\mathrm{x}−\mathrm{3}\mid<\mathrm{0}.\mathrm{1} \\ $$

Question Number 91469 Answers: 0 Comments: 3

−5<((4−3x)/2)<l

$$−\mathrm{5}<\frac{\mathrm{4}−\mathrm{3x}}{\mathrm{2}}<\mathrm{l} \\ $$

Question Number 91468 Answers: 0 Comments: 0

Question Number 91464 Answers: 0 Comments: 12

Find the greatest coefficient in the expansion of (3 − 2x)^(−7)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{3}\:\:−\:\:\mathrm{2x}\right)^{−\mathrm{7}} \\ $$

Question Number 91465 Answers: 1 Comments: 1

Question Number 91460 Answers: 1 Comments: 0

one of the conditions of the inflection point is inflection tangent. what is inflection tangent?

$${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$

Question Number 91452 Answers: 2 Comments: 1

((−1))^(1/4) =?

$$\:\:\:\sqrt[{\mathrm{4}}]{−\mathrm{1}}\:=? \\ $$

Question Number 91448 Answers: 0 Comments: 3

prove that 1+x^(111) +x^(222) +x^(333) +x^(444) divides 1+ x^(111) +x^(222) +x^(333) +.......+x^(999)

$${prove}\:{that}\:\mathrm{1}+{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +{x}^{\mathrm{444}} \:\:{divides}\:\mathrm{1}+\:{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +.......+{x}^{\mathrm{999}} \\ $$

Question Number 91446 Answers: 0 Comments: 1

Question Number 91439 Answers: 1 Comments: 2

solve 2x^(99) +3x^(98) +2x^(97) +3x^(96) +.....2x+3=0 in R

$${solve}\:\mathrm{2}{x}^{\mathrm{99}} +\mathrm{3}{x}^{\mathrm{98}} +\mathrm{2}{x}^{\mathrm{97}} +\mathrm{3}{x}^{\mathrm{96}} +.....\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:{in}\:\mathbb{R} \\ $$

Question Number 91671 Answers: 0 Comments: 2

show that (x)^(1/(ln(x))) =e

$${show}\:{that} \\ $$$$\sqrt[{{ln}\left({x}\right)}]{{x}}={e} \\ $$

Question Number 91419 Answers: 0 Comments: 1

lim_(x→0) (1/(sin^4 x))(sin ((x/(1+x)))−((sin x)/(1+sin x)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{4}} {x}}\left(\mathrm{sin}\:\left(\frac{{x}}{\mathrm{1}+{x}}\right)−\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\right) \\ $$

Question Number 91417 Answers: 0 Comments: 1

y′+2y=e^(−x)

$${y}'+\mathrm{2}{y}={e}^{−{x}} \\ $$

Question Number 91422 Answers: 0 Comments: 0

(dy/dx) = ((x^2 +y^2 )/(x^2 −y^2 ))

$$\frac{{dy}}{{dx}}\:=\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$

Question Number 91399 Answers: 2 Comments: 13

Question Number 91395 Answers: 0 Comments: 0

∫_0 ^π ((∣x∣sin^2 x)/(1+2∣cos x∣sin x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mid{x}\mid\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{2}\mid\mathrm{cos}\:{x}\mid\mathrm{sin}\:{x}}{dx} \\ $$

Question Number 91390 Answers: 1 Comments: 3

ABCDEF is a 6 digit number, ABC and DEF are 3 digit numbers. find ABCDEF satisfying: 1) ABCDEF=1×ABC×DEF 2) ABCDEF=2×ABC×DEF 3) ABCDEF=3×ABC×DEF 4) ABCDEF=4×ABC×DEF 5) ABCDEF=5×ABC×DEF 6) ABCDEF=6×ABC×DEF 7) ABCDEF=7×ABC×DEF 8) ABCDEF=8×ABC×DEF 9) ABCDEF=9×ABC×DEF

$${ABCDEF}\:{is}\:{a}\:\mathrm{6}\:{digit}\:{number}, \\ $$$${ABC}\:{and}\:{DEF}\:{are}\:\mathrm{3}\:{digit}\:{numbers}. \\ $$$${find}\:{ABCDEF}\:\:{satisfying}: \\ $$$$\left.\mathrm{1}\right)\:\:\:{ABCDEF}=\mathrm{1}×{ABC}×{DEF} \\ $$$$\left.\mathrm{2}\right)\:\:\:{ABCDEF}=\mathrm{2}×{ABC}×{DEF} \\ $$$$\left.\mathrm{3}\right)\:\:\:{ABCDEF}=\mathrm{3}×{ABC}×{DEF} \\ $$$$\left.\mathrm{4}\right)\:\:\:{ABCDEF}=\mathrm{4}×{ABC}×{DEF} \\ $$$$\left.\mathrm{5}\right)\:\:\:{ABCDEF}=\mathrm{5}×{ABC}×{DEF} \\ $$$$\left.\mathrm{6}\right)\:\:\:{ABCDEF}=\mathrm{6}×{ABC}×{DEF} \\ $$$$\left.\mathrm{7}\right)\:\:\:{ABCDEF}=\mathrm{7}×{ABC}×{DEF} \\ $$$$\left.\mathrm{8}\right)\:\:\:{ABCDEF}=\mathrm{8}×{ABC}×{DEF} \\ $$$$\left.\mathrm{9}\right)\:\:\:{ABCDEF}=\mathrm{9}×{ABC}×{DEF} \\ $$

Question Number 91421 Answers: 2 Comments: 2

∫_1 ^3 (1/(x(√(3x^2 +2x−1))))dx

$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{1}}{{x}\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}{dx} \\ $$

Question Number 91384 Answers: 0 Comments: 4

particular integral y′′+3y′+2y = 4cos^2 x

$${particular}\:{integral}\: \\ $$$${y}''+\mathrm{3}{y}'+\mathrm{2}{y}\:=\:\mathrm{4cos}\:^{\mathrm{2}} {x} \\ $$

Question Number 91378 Answers: 1 Comments: 6

Question Number 91377 Answers: 0 Comments: 1

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