Question and Answers Forum

AllQuestion and Answers: Page 1305

Question Number 83864 Answers: 0 Comments: 3

what Maclaurin series of function tan (x)?

$$\mathrm{what}\:\mathrm{Maclaurin}\:\mathrm{series}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)? \\ $$

Question Number 83861 Answers: 0 Comments: 3

An object of mass 7kg is sliding down a frictionless 20m inclined plane. Calculate the speed of the object when it reaches the ground.

$$\mathrm{An}\:\mathrm{object}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{7kg}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{down} \\ $$$$\mathrm{a}\:\mathrm{frictionless}\:\mathrm{20m}\:\mathrm{inclined}\:\mathrm{plane}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 83859 Answers: 0 Comments: 1

lim_(x→0) ((1/x^2 )− cot^2 x)= ?

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

Question Number 83852 Answers: 0 Comments: 3

f(α)=∫_0 ^∞ ((e^(−αx) sin(x))/x)dx

$${f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\alpha{x}} {sin}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 83850 Answers: 2 Comments: 1

Find the maximum value of the function f, defined by f(x) = (x/(1+ x^2 )) , x∈R

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{f},\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:{f}\left({x}\right)\:=\:\frac{{x}}{\mathrm{1}+\:{x}^{\mathrm{2}} }\:,\:{x}\in\mathbb{R} \\ $$

Question Number 83849 Answers: 0 Comments: 3

Gven that y = e^(−x) sinbx ,where b is a constant,show that (d^2 y/dx^2 ) + 2(dy/dx) + (1 + b^2 )y = 0.

$$\mathrm{Gven}\:\mathrm{that}\:{y}\:=\:{e}^{−{x}} \mathrm{sin}{bx}\:,\mathrm{where}\:{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\mathrm{show}\:\mathrm{that} \\ $$$$\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\frac{{dy}}{{dx}}\:+\:\left(\mathrm{1}\:+\:{b}^{\mathrm{2}} \right){y}\:=\:\mathrm{0}. \\ $$

Question Number 83842 Answers: 0 Comments: 4

∫((ln(x))/(ln(6x−x^2 )))dx

$$\int\frac{{ln}\left({x}\right)}{{ln}\left(\mathrm{6}{x}−{x}^{\mathrm{2}} \right)}{dx} \\ $$

Question Number 83834 Answers: 1 Comments: 2

Question Number 83824 Answers: 2 Comments: 1

Question Number 83822 Answers: 1 Comments: 1

Question Number 83819 Answers: 1 Comments: 0

If the function of f is continous in R and ∫ _0 ^( x) f(t)dt = ∫ _x ^( 1) t^2 f(t) dt + 2x^2 +4x+c , ∀x∈R. The value of constant c is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\:\mathrm{is}\:\mathrm{continous} \\ $$$$\mathrm{in}\:\mathbb{R}\:\mathrm{and}\:\int\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\:}}\:\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}\:=\:\int\underset{\mathrm{x}} {\overset{\:\mathrm{1}} {\:}}\mathrm{t}^{\mathrm{2}} \mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:+\: \\ $$$$\mathrm{2x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{c}\:,\:\forall\mathrm{x}\in\mathbb{R}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{constant}\:\mathrm{c}\:\mathrm{is}\: \\ $$

Question Number 83812 Answers: 0 Comments: 0

Question Number 83811 Answers: 0 Comments: 2

Question Number 83807 Answers: 2 Comments: 1

Evaluate: ∫ (( 1)/(ax^2 +bx+c))dx

$$\:\:\boldsymbol{\mathrm{Evaluate}}: \\ $$$$\:\:\int\:\:\frac{\:\mathrm{1}}{\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{c}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 83805 Answers: 3 Comments: 1

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

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}\:{dx} \\ $$

Question Number 83892 Answers: 0 Comments: 0

∫(du/(u−u^2 ))

$$\int\frac{\mathrm{du}}{\mathrm{u}−\mathrm{u}^{\mathrm{2}} } \\ $$

Question Number 83891 Answers: 0 Comments: 3

1111^(2019) mod 11111=....?

$$ \\ $$$$ \\ $$$$\mathrm{1111}^{\mathrm{2019}} \:\mathrm{mod}\:\mathrm{11111}=....? \\ $$

Question Number 83791 Answers: 2 Comments: 2

Let x, y are two different real numbers satisfy the equation (√(y+4)) = x−4 and (√(x+4)) = y−4. The value of x^3 +y^3 mod(x^3 y^3 ) is

$$\mathrm{Let}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\:\mathrm{two}\:\mathrm{different}\:\mathrm{real} \\ $$$$\mathrm{numbers}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{y}+\mathrm{4}}\:=\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\sqrt{\mathrm{x}+\mathrm{4}}\:=\:\mathrm{y}−\mathrm{4}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \:\mathrm{mod}\left(\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$

Question Number 83787 Answers: 1 Comments: 0

find the value of abc if (√(2+(√(2^2 +(√(2^3 +2^4 +(√(...)))))))) = (((√a)+(√b))/c)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{abc}\:\mathrm{if}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}^{\mathrm{2}} +\sqrt{\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +\sqrt{...}}}}\:=\:\frac{\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}}{\mathrm{c}} \\ $$

Question Number 83786 Answers: 2 Comments: 0

(x^2 /(log_((5−x)) (x))) ≤ (5x−4) log_x (5−x)

$$\frac{{x}^{\mathrm{2}} }{\mathrm{log}_{\left(\mathrm{5}−{x}\right)} \:\left({x}\right)}\:\leqslant\:\left(\mathrm{5}{x}−\mathrm{4}\right)\:\mathrm{log}_{{x}} \:\left(\mathrm{5}−{x}\right)\: \\ $$

Question Number 83782 Answers: 0 Comments: 1

f^((5)) (x) = 4^(−sin x) f^((7)) (x) =?

$$\mathrm{f}^{\left(\mathrm{5}\right)} \:\left(\mathrm{x}\right)\:=\:\mathrm{4}^{−\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{x}\right)\:=?\: \\ $$

Question Number 83781 Answers: 1 Comments: 2

∫ _0^(π/2) (1/(4sin^2 x+5cos^2 x)) dx

$$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 83774 Answers: 1 Comments: 0

Given 2(√(log_3 x−1)) − log_3 x^3 +8 > 0 have the solution a ≤ x < b. what is b ?

$$\mathrm{Given}\:\mathrm{2}\sqrt{\mathrm{log}_{\mathrm{3}} \:{x}−\mathrm{1}}\:−\:\mathrm{log}_{\mathrm{3}} \:{x}^{\mathrm{3}} \:+\mathrm{8}\:>\:\mathrm{0} \\ $$$${have}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{a}\:\leqslant\:{x}\:<\:{b}.\: \\ $$$${what}\:{is}\:{b}\:?\: \\ $$

Question Number 83767 Answers: 2 Comments: 1

Question Number 83759 Answers: 2 Comments: 3

3^x 8^(x/(x+2)) =6

$$\mathrm{3}^{{x}} \:\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6} \\ $$

Question Number 83756 Answers: 0 Comments: 3

Find all real solutions of (x, y) such that x + 3y + (4/(x + y)) = 5 y + 3x + (5/(x + y)) = 7

$${Find}\:\:{all}\:\:{real}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\mathrm{3}{y}\:+\:\frac{\mathrm{4}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:{y}\:+\:\mathrm{3}{x}\:+\:\frac{\mathrm{5}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{7} \\ $$

Pg 1300 Pg 1301 Pg 1302 Pg 1303 Pg 1304 Pg 1305 Pg 1306 Pg 1307 Pg 1308 Pg 1309

Contact: info@tinkutara.com