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AllQuestion and Answers: Page 1104

Question Number 106077 Answers: 0 Comments: 0

Given Σ_(n = 0) ^∞ cos^(2n) (θ) = 5. find the value of cos 2θ+cos 4θ+cos 8θ+cos 16θ+cos 32θ+...= (a) (1/5) (b) (3/5) (c) 2 (d) 1 (e) 3

$$\mathcal{G}\mathrm{iven}\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:^{\mathrm{2n}} \left(\theta\right)\:=\:\mathrm{5}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{16}\theta+\mathrm{cos} \\ $$$$\mathrm{32}\theta+...= \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{1}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{3} \\ $$

Question Number 106076 Answers: 2 Comments: 0

solve this pls x^x^(1/2) =(1/2)

$${solve}\:{this}\:{pls} \\ $$$${x}^{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} } =\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 106075 Answers: 1 Comments: 0

∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=?

$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$

Question Number 106072 Answers: 2 Comments: 0

Question Number 106070 Answers: 0 Comments: 0

Question Number 106065 Answers: 0 Comments: 0

x^2 (d^2 y/dx^2 ) −x (dy/dx) +y = x

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

Question Number 106044 Answers: 1 Comments: 0

Given f(x)=2x+m, f^(2 ) (x)=px+6 Find the value of m and p.

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{m},\:\mathrm{f}^{\mathrm{2}\:} \left(\mathrm{x}\right)=\mathrm{px}+\mathrm{6} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{p}. \\ $$

Question Number 106039 Answers: 3 Comments: 0

if (f o g )(x) = x and f′(x)=1 + (f(x))^2 then g′(2) = ....

$${if}\:\:\left({f}\:{o}\:{g}\:\right)\left({x}\right)\:=\:{x}\:\:{and}\:{f}'\left({x}\right)=\mathrm{1}\:+\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \\ $$$${then}\:{g}'\left(\mathrm{2}\right)\:=\:.... \\ $$$$ \\ $$

Question Number 106033 Answers: 16 Comments: 0

Question Number 106032 Answers: 0 Comments: 2

Version 2.127 is added. • automatically scroll hine in horizontal direction (requested by Mr W) • automatically scrolls to new line to bring newly added line in focus.

$$\mathrm{Version}\:\mathrm{2}.\mathrm{127}\:\mathrm{is}\:\mathrm{added}. \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scroll}\:\mathrm{hine}\:\mathrm{in}\:\mathrm{horizontal} \\ $$$$\:\:\:\mathrm{direction}\:\left(\mathrm{requested}\:\mathrm{by}\:\mathrm{Mr}\:\mathrm{W}\right) \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scrolls}\:\mathrm{to}\:\mathrm{new}\:\mathrm{line}\:\mathrm{to} \\ $$$$\:\:\:\mathrm{bring}\:\mathrm{newly}\:\mathrm{added}\:\mathrm{line}\:\mathrm{in}\:\mathrm{focus}. \\ $$

Question Number 106029 Answers: 1 Comments: 1

Question Number 106024 Answers: 2 Comments: 1

log _4 (5x−6).log _x (256)=8

$$\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{5x}−\mathrm{6}\right).\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{256}\right)=\mathrm{8} \\ $$

Question Number 106023 Answers: 1 Comments: 2

Given that f(0)≠0 for all x,y∈R; 2f(x)f(y)=f(x+y)+f(x−y), express f(2x) in term of f(x).

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{0}\right)\neq\mathrm{0}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\in\mathbb{R}; \\ $$$$\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{y}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right),\: \\ $$$$\mathrm{express}\:\mathrm{f}\left(\mathrm{2x}\right)\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$

Question Number 106022 Answers: 0 Comments: 0

Question Number 106019 Answers: 1 Comments: 0

Question Number 106010 Answers: 1 Comments: 0

∫ ((1+x+x^2 )/(x^2 (x+1))) dx

$$\int\:\frac{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\: \\ $$

Question Number 106017 Answers: 1 Comments: 0

Determine x & y, such that: lcm(x,y)−gcd(x,y)=x+y.

$$\mathcal{D}{etermine}\:{x}\:\&\:{y},\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left({x},{y}\right)−\mathrm{gcd}\left({x},{y}\right)={x}+{y}. \\ $$

Question Number 106005 Answers: 3 Comments: 0

(1) y′ = ((y−2x)/(2y+x)) (2) lim_(x→0) ((2^x −cos x)/(sin x))

$$\left(\mathrm{1}\right)\:\mathrm{y}'\:=\:\frac{\mathrm{y}−\mathrm{2x}}{\mathrm{2y}+\mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{x}} −\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}} \\ $$

Question Number 106001 Answers: 2 Comments: 0

Question Number 105994 Answers: 1 Comments: 1

Given { ((2log _5 (x+2)−log _5 (y)+(1/2)=0)),((log _5 (x^2 +2x−2)=0 )) :} find the value of y

$$\mathbb{G}{iven}\:\begin{cases}{\mathrm{2log}\:_{\mathrm{5}} \left({x}+\mathrm{2}\right)−\mathrm{log}\:_{\mathrm{5}} \left({y}\right)+\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0}}\\{\mathrm{log}\:_{\mathrm{5}} \left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}\right)=\mathrm{0}\:}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{y}\: \\ $$

Question Number 105992 Answers: 1 Comments: 0

Question Number 105990 Answers: 1 Comments: 0

lim_(x→0) (cosec^2 2x − (1/(4x^2 ))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cosec}\:^{\mathrm{2}} \mathrm{2}{x}\:−\:\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}} }\right)\:=\:? \\ $$

Question Number 105985 Answers: 1 Comments: 0

Question Number 105983 Answers: 1 Comments: 1

∫ ((sin x dx)/(6−sin^2 x)) ?

$$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{\mathrm{6}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:?\:\: \\ $$

Question Number 105969 Answers: 3 Comments: 0

∫((sinx+cosx)/(√(1+sin2x)))dx

$$\int\frac{\mathrm{sinx}+\mathrm{cosx}}{\sqrt{\mathrm{1}+\mathrm{sin2x}}}\mathrm{dx} \\ $$

Question Number 105952 Answers: 2 Comments: 0

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