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Question Number 111374    Answers: 1   Comments: 1

Question Number 111365    Answers: 0   Comments: 0

Question Number 111471    Answers: 0   Comments: 0

using power expension, compute the follplowing limit as a function of α>0 lim_(x→0^+ ) ((x^(7/2) ln(x)−sinh(x^2 )+cosh(ln(1−(√2)x))−1)/x^α )

$${using}\:{power}\:{expension},\:{compute}\:{the}\:{follplowing} \\ $$$${limit}\:{as}\:{a}\:{function}\:{of}\:\alpha>\mathrm{0} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{{x}^{\frac{\mathrm{7}}{\mathrm{2}}} {ln}\left({x}\right)−{sinh}\left({x}^{\mathrm{2}} \right)+{cosh}\left({ln}\left(\mathrm{1}−\sqrt{\mathrm{2}}{x}\right)\right)−\mathrm{1}}{{x}^{\alpha} } \\ $$

Question Number 111357    Answers: 0   Comments: 0

∫_0 ^1 ((tan^(−1) x)/(1+x^3 ))dx

$$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{tan}^{−\mathrm{1}} {x}}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 111351    Answers: 2   Comments: 0

(√(bemath)) lim_(x→−∞) ((x−(√(4x^2 +1)))/( (√(x^2 +2x+1)))) ?

$$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{x}−\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}}}\:? \\ $$

Question Number 111347    Answers: 0   Comments: 0

convert the plane with cartesian equation: x−3y + 2z = 7 into its vector parametric form.

$$\mathrm{convert}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{with}\:\mathrm{cartesian}\:\mathrm{equation}:\:{x}−\mathrm{3}{y}\:+\:\mathrm{2}{z}\:=\:\mathrm{7} \\ $$$$\:\mathrm{into}\:\mathrm{its}\:\mathrm{vector}\:\mathrm{parametric}\:\mathrm{form}. \\ $$$$ \\ $$

Question Number 111344    Answers: 0   Comments: 3

(√3)!=?

$$\sqrt{\mathrm{3}}!=? \\ $$

Question Number 111343    Answers: 0   Comments: 1

i!=?

$${i}!=? \\ $$

Question Number 111342    Answers: 1   Comments: 0

When the terms of a Geometric Progression(GP) with common ratio r=2 is added to the corresponding terms of an Arithmetic Provression (AP), a new sequence is formed. If the first terms of the GP and AP are the same and the first three terms of the new sequence are 3, 7 and 11 respectively, find the n^(th) term of the seauence.

$$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\left(\mathrm{GP}\right) \\ $$$$\mathrm{with}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{Arithmetic}\:\mathrm{Provression}\:\left(\mathrm{AP}\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{seauence}. \\ $$

Question Number 111340    Answers: 1   Comments: 2

Question Number 111330    Answers: 0   Comments: 0

(√(bemath)) (1/x) (dy/dx) + (1/y) = (1/(y^2 ln (x)))

$$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\frac{\mathrm{1}}{\mathrm{x}}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:=\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} \:\mathrm{ln}\:\left(\mathrm{x}\right)} \\ $$

Question Number 111326    Answers: 2   Comments: 0

(√(bemath)) lim_(x→0) ((1/(x sin^(−1) (x))) − (1/x^2 ) ) =?

$$\:\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)}\:−\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:\right)\:=? \\ $$

Question Number 111313    Answers: 4   Comments: 0

(√(bemath)) (1)lim_(n→∞) (((n+1)^5 +(n+2)^5 +(n+3)^5 +...+(2n)^5 )/n^6 )? (2) ∫ ((√(x^2 −a^2 ))/x^4 ) dx

$$\:\:\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\left(\mathrm{1}\right)\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{5}} +\left(\mathrm{n}+\mathrm{2}\right)^{\mathrm{5}} +\left(\mathrm{n}+\mathrm{3}\right)^{\mathrm{5}} +...+\left(\mathrm{2n}\right)^{\mathrm{5}} }{\mathrm{n}^{\mathrm{6}} }? \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx}\:\: \\ $$

Question Number 111277    Answers: 1   Comments: 0

In a quadrilateral ABCD, ∠B is a right angle, diagonal AC is perpendicular to CD,BC=21cm,CD=14cm and AD=31cm. Find the area of ABCD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{quadrilateral}\:\mathrm{ABCD},\:\angle\mathrm{B}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{right}\:\mathrm{angle},\:\mathrm{diagonal}\:\mathrm{AC}\:\mathrm{is} \\ $$$$\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{CD},\mathrm{BC}=\mathrm{21cm},\mathrm{CD}=\mathrm{14cm}\:\mathrm{and} \\ $$$$\mathrm{AD}=\mathrm{31cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{ABCD}. \\ $$

Question Number 111267    Answers: 1   Comments: 0

Question Number 111264    Answers: 1   Comments: 1

Question Number 111259    Answers: 1   Comments: 1

lim_(x→0^+ ) ((sin 2x)/( (√(3x)))) ?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}}{\:\sqrt{\mathrm{3x}}}\:? \\ $$

Question Number 111218    Answers: 1   Comments: 0

Question Number 111216    Answers: 3   Comments: 2

Question Number 111213    Answers: 2   Comments: 0

Question Number 111209    Answers: 0   Comments: 6

find the ODEs of y=Ae^x +Bxe^x +Ce^(−2x) +De^(3x)

$${find}\:{the}\:{ODEs}\:{of}\: \\ $$$${y}={Ae}^{{x}} +{Bxe}^{{x}} +{Ce}^{−\mathrm{2}{x}} +{De}^{\mathrm{3}{x}} \\ $$

Question Number 111208    Answers: 1   Comments: 3

let p a prime number s.t p≥7 and a=333......3_(p−1 times) Show that 11∣a.

$$\:\mathrm{let}\:{p}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{s}.\mathrm{t}\:{p}\geqslant\mathrm{7}\:\mathrm{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}=\underset{{p}−\mathrm{1}\:{times}} {\mathrm{333}......\mathrm{3}} \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{11}\mid{a}. \\ $$

Question Number 111235    Answers: 1   Comments: 1

Question Number 111206    Answers: 1   Comments: 0

∫ (dx/(x^3 +3x−5))

$$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}} \\ $$

Question Number 111205    Answers: 0   Comments: 1

An 800kg car is towed up an 8^0 hill by a rope attached to a truck. The tension in the rope is 2000N and there is no frictional resistance to the car motion. How much time is needed to tow the car for 50m starting from rest?

$$\mathrm{An}\:\mathrm{800kg}\:\mathrm{car}\:\mathrm{is}\:\mathrm{towed}\:\mathrm{up}\:\mathrm{an}\:\mathrm{8}^{\mathrm{0}} \:\mathrm{hill}\:\mathrm{by}\:\mathrm{a}\:\mathrm{rope}\: \\ $$$$\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{truck}.\:\mathrm{The}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{rope} \\ $$$$\mathrm{is}\:\mathrm{2000N}\:\mathrm{and}\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{frictional}\:\mathrm{resistance} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{car}\:\mathrm{motion}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{time}\:\mathrm{is}\:\mathrm{needed}\: \\ $$$$\mathrm{to}\:\mathrm{tow}\:\mathrm{the}\:\mathrm{car}\:\mathrm{for}\:\mathrm{50m}\:\mathrm{starting}\:\mathrm{from}\:\mathrm{rest}? \\ $$

Question Number 112193    Answers: 0   Comments: 1

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