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Question Number 169480 Answers: 1 Comments: 0

Question Number 169479 Answers: 2 Comments: 2

lim_(x→4) (((cos a)^x −(sin a)^x −cos 2a)/(x−4)) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:{a}\right)^{{x}} −\left(\mathrm{sin}\:{a}\right)^{{x}} −\mathrm{cos}\:\mathrm{2}{a}}{{x}−\mathrm{4}}\:=? \\ $$

Question Number 169466 Answers: 1 Comments: 0

Question Number 169458 Answers: 2 Comments: 1

Question Number 169448 Answers: 1 Comments: 6

Question Number 169447 Answers: 0 Comments: 0

The equation of the curve is given y=(x^3 /6)−((5x^2 )/2)−6x−1 1) Determine the critical points 2) Distinguish between these points 3) Determine the Maximum and minimum values 4) Determine the value of x and y at point of inflexion Mastermind

$${The}\:{equation}\:{of}\:{the}\:{curve}\:{is}\:{given} \\ $$$${y}=\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{6}{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{Determine}\:{the}\:{critical}\:{points} \\ $$$$\left.\mathrm{2}\right)\:{Distinguish}\:{between}\:{these}\:{points} \\ $$$$\left.\mathrm{3}\right)\:{Determine}\:{the}\:{Maximum}\:{and} \\ $$$${minimum}\:{values} \\ $$$$\left.\mathrm{4}\right)\:{Determine}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$$${at}\:{point}\:{of}\:{inflexion}\: \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169445 Answers: 0 Comments: 8

let x and y be positive reals such that x^3 + y^3 + (x+y)^3 +30xy = 2000 show that x+y = 10

$$ \\ $$$$\:\:\:\mathrm{let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} \:+\mathrm{30xy}\:=\:\mathrm{2000} \\ $$$$\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{10} \\ $$

Question Number 169439 Answers: 1 Comments: 0

Question Number 169438 Answers: 0 Comments: 1

Question Number 169436 Answers: 1 Comments: 1

Question Number 169429 Answers: 1 Comments: 0

(√(220+30(√(35))))=

$$\sqrt{\mathrm{220}+\mathrm{30}\sqrt{\mathrm{35}}}= \\ $$

Question Number 169421 Answers: 0 Comments: 0

Question Number 169413 Answers: 0 Comments: 0

Question Number 169412 Answers: 0 Comments: 1

Question Number 169407 Answers: 1 Comments: 0

Question Number 169389 Answers: 0 Comments: 1

1. 2(√y) dx = dy 2. (x^2 + y^2 )dx = 2xydy 3. xdx + (1/y) dy = 0 4. dy = 3x^2 dx 5. 2y^2 dx + x(1 + y^2 ) dy = 0 6. 4x^3 dx + dy = 0

$$\mathrm{1}.\:\mathrm{2}\sqrt{\mathrm{y}}\:\mathrm{dx}\:=\:\mathrm{dy} \\ $$$$\mathrm{2}.\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}\:=\:\mathrm{2xydy} \\ $$$$\mathrm{3}.\:\mathrm{xdx}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{4}.\:\mathrm{dy}\:=\:\mathrm{3x}^{\mathrm{2}} \:\mathrm{dx} \\ $$$$\mathrm{5}.\:\mathrm{2y}^{\mathrm{2}} \mathrm{dx}\:+\:\mathrm{x}\left(\mathrm{1}\:+\:\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{6}.\:\mathrm{4x}^{\mathrm{3}} \mathrm{dx}\:+\:\mathrm{dy}\:=\:\mathrm{0} \\ $$

Question Number 169382 Answers: 1 Comments: 7

find the value of [v] if v denotes maximum value of x^2 + y^2 , where (x+5)^2 + (y−12)^2 = 14 (hint [•] repersent greatest integer function of “ •”)

Question Number 169391 Answers: 1 Comments: 2

Question Number 169396 Answers: 0 Comments: 14

(√x)+1=0 find x Mastermind

$$\sqrt{{x}}+\mathrm{1}=\mathrm{0} \\ $$$${find}\:{x} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169397 Answers: 2 Comments: 0

Question Number 169366 Answers: 0 Comments: 1

Differentiate from first principle y=log_x a Mastermind

$${Differentiate}\:{from}\:{first}\:{principle} \\ $$$${y}={log}_{{x}} {a} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169364 Answers: 1 Comments: 0

Show that the differential equation y′′ −4y′+4y=0 is satisfied when y=xe^(2x) Mastermind

$${Show}\:{that}\:{the}\:{differential}\:{equation} \\ $$$${y}''\:−\mathrm{4}{y}'+\mathrm{4}{y}=\mathrm{0}\:{is}\:{satisfied}\:{when} \\ $$$${y}={xe}^{\mathrm{2}{x}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169362 Answers: 2 Comments: 0

∫tan(2x+3)dx Mastermind

$$\int{tan}\left(\mathrm{2}{x}+\mathrm{3}\right){dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169358 Answers: 1 Comments: 0

Differentiate from first principle y=(1/(x^2 +5))

$${Differentiate}\:{from}\:{first}\:{principle} \\ $$$${y}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{5}} \\ $$

Question Number 169356 Answers: 3 Comments: 0

1. y = arcsin(sinx) ⇒ y^′ =? 2. y = sin (√(x + 1)) ⇒ y^′ =? 3. y = ln^5 sinx ⇒ y^′ =? 4. y = cos(2x + 3) ⇒ y^′ =?

$$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{arcsin}\left(\mathrm{sinx}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\mathrm{sin}\:\sqrt{\mathrm{x}\:+\:\mathrm{1}}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{ln}^{\mathrm{5}} \:\mathrm{sinx}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{4}.\:\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2x}\:+\:\mathrm{3}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$

Question Number 169354 Answers: 1 Comments: 0

1. ∫_0 ^1 (dx/(1 + x)) 2. ∫_0 ^( 1) (6 - x^2 )dx 3. ∫_0 ^( (π/2)) ((cosx)/(1 + sinx)) dx

$$\mathrm{1}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{x}} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{6}\:-\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{cosx}}{\mathrm{1}\:+\:\mathrm{sinx}}\:\mathrm{dx} \\ $$

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