Question and Answers Forum

AllQuestion and Answers: Page 1440

Question Number 64791 Answers: 0 Comments: 1

Question Number 64788 Answers: 0 Comments: 2

two consercutive integers between which a root of the equation lie are: x^2 +3x+2=0

$${two}\:{consercutive}\:{integers}\:{between}\:{which}\:{a}\:{root}\:{of}\:{the}\:{equation}\:{lie}\:{are}: \\ $$$${x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 64785 Answers: 1 Comments: 0

Question Number 64778 Answers: 1 Comments: 2

Question Number 64775 Answers: 1 Comments: 1

Question Number 64773 Answers: 1 Comments: 0

sin^(−1) (1/(√(5)))+cot^(−1) 3

$$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}/\sqrt{\left.\mathrm{5}\right)}+\mathrm{cot}^{−\mathrm{1}} \mathrm{3}\right. \\ $$

Question Number 64762 Answers: 1 Comments: 1

Given that g(x)=(2/((1+x)(1+3x^2 )) a) express g(x) in partial fractions. b) evaluate ∫_0 ^1 g((x) dx.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$

Question Number 64759 Answers: 0 Comments: 0

∫((ln(ln(x)))/((ln(x))^n )) dx , n≠1

$$\int\frac{{ln}\left({ln}\left({x}\right)\right)}{\left({ln}\left({x}\right)\right)^{{n}} }\:{dx}\:\:\:,\:\:\:{n}\neq\mathrm{1} \\ $$

Question Number 64758 Answers: 2 Comments: 0

Solve: x^4 + 5x^3 − 4x^2 + 7x − 1 = 0

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{5x}^{\mathrm{3}} \:−\:\mathrm{4x}^{\mathrm{2}} \:+\:\mathrm{7x}\:−\:\mathrm{1}\:\:=\:\:\mathrm{0} \\ $$

Question Number 64751 Answers: 0 Comments: 1

Find the force parallel to the slope required to move a body of mass 2kg up a slope inclined at 30° to the horizontal with an acceleration oc 2m/s^2 if the frictional force is 10N.

$${Find}\:{the}\:{force}\:{parallel}\:{to}\:{the}\:{slope} \\ $$$${required}\:{to}\:{move}\:{a}\:{body}\:{of}\:{mass}\:\mathrm{2}{kg} \\ $$$${up}\:{a}\:{slope}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the} \\ $$$${horizontal}\:{with}\:{an}\:{acceleration}\:{oc}\:\mathrm{2}{m}/{s}^{\mathrm{2}} \\ $$$${if}\:{the}\:{frictional}\:{force}\:{is}\:\mathrm{10}{N}. \\ $$

Question Number 64750 Answers: 0 Comments: 0

A body of mass 4kg is at the point of slipping down a plane which is inclined at 30° to the horizontal.What is the force parallel to the plane that will just move it up?

$${A}\:{body}\:{of}\:{mass}\:\mathrm{4}{kg}\:{is}\:{at}\:{the}\:{point}\:{of} \\ $$$${slipping}\:{down}\:{a}\:{plane}\:{which}\:{is} \\ $$$${inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{horizontal}.{What} \\ $$$${is}\:{the}\:{force}\:{parallel}\:{to}\:{the}\:{plane}\:{that} \\ $$$${will}\:{just}\:{move}\:{it}\:{up}? \\ $$

Question Number 64745 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((sin(lnx))/(lnx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$

Question Number 64744 Answers: 2 Comments: 0

solve^3 (√(1+x))+^3 (√(1−x))=2

$${solve}\:^{\mathrm{3}} \sqrt{\mathrm{1}+{x}}+^{\mathrm{3}} \sqrt{\mathrm{1}−{x}}=\mathrm{2} \\ $$

Question Number 64871 Answers: 0 Comments: 5

any hint about how to prove by induction in the Sigma notion topic? like in Σ

$${any}\:{hint}\:{about}\:{how}\:{to}\:{prove}\:{by}\:{induction}\:{in}\:{the}\:{Sigma}\:{notion}\:{topic}? \\ $$$${like}\:{in}\:\Sigma \\ $$

Question Number 64873 Answers: 0 Comments: 4

let f(x) =∫_0 ^π (dt/(x+sint)) with xreal 1) find a explicit form of f(x) 2) find also g(x) =∫_0 ^π (dt/((x+sint)^2 )) 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^π (dt/(3+sint)) and ∫_0 ^π (dt/((3+sint)^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{{x}+{sint}}\:\:\:{with}\:{xreal} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left({x}+{sint}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\mathrm{3}+{sint}}\:\:{and}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left(\mathrm{3}+{sint}\right)^{\mathrm{2}} } \\ $$

Question Number 64872 Answers: 0 Comments: 4

Given that y = (cosx^ )^(sinx) find (dy/dx) and lim_(x→0) y

$${Given}\:{that}\: \\ $$$$\:{y}\:=\:\left({cosx}^{} \right)^{{sinx}} \:\:{find}\:\frac{{dy}}{{dx}} \\ $$$${and}\: \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{y} \\ $$

Question Number 64735 Answers: 0 Comments: 2

∫tanθ/1+^− sinθ dθ

$$\int{tan}\theta/\mathrm{1}\overset{−} {+}{sin}\theta\:{d}\theta \\ $$

Question Number 64733 Answers: 0 Comments: 0

∫(secθtanθ)dθ/secθ+^− tanθ

$$\int\left({sec}\theta{tan}\theta\right){d}\theta/{sec}\theta\overset{−} {+}{tan}\theta \\ $$

Question Number 64730 Answers: 2 Comments: 0