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Relation and FunctionsQuestion and Answers: Page 5

Question Number 161485 Answers: 0 Comments: 0

Find range of function y=((cos 4x+4sin 4x+1)/(cos 4x+2))

$$\:\mathrm{Find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\:\mathrm{y}=\frac{\mathrm{cos}\:\mathrm{4x}+\mathrm{4sin}\:\mathrm{4x}+\mathrm{1}}{\mathrm{cos}\:\mathrm{4x}+\mathrm{2}} \\ $$

Question Number 161442 Answers: 1 Comments: 0

Use the binomial theorem to write the first four terms of the expansion of (√(2+3x−x^2 ))

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{write} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\sqrt{\mathrm{2}+\mathrm{3}{x}−{x}^{\mathrm{2}} } \\ $$

Question Number 161391 Answers: 0 Comments: 4

f^( 3) (x)+x^2 f(x)=2x^3 +4x^2 +3x+1 ∀x∈R

$$\:\:{f}^{\:\mathrm{3}} \left({x}\right)+{x}^{\mathrm{2}} \:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1} \\ $$$$\:\forall{x}\in\mathbb{R}\: \\ $$

Question Number 161387 Answers: 0 Comments: 0

sin(√(1+π^2 n^2 )) ∼ (((−1)^n )/(2πn)) ?

$$\:{sin}\sqrt{\mathrm{1}+\pi^{\mathrm{2}} {n}^{\mathrm{2}} }\:\sim\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}\pi{n}}\:\:? \\ $$

Question Number 161114 Answers: 0 Comments: 0

Let f(x)= sin^3 (2x) for −(π/4)≤x≤(π/4) then Df^(−1) ((1/8))=(a/(b(√b))) so { ((a=?)),((b=?)) :}

$$\:\:{Let}\:{f}\left({x}\right)=\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)\:{for}\:−\frac{\pi}{\mathrm{4}}\leqslant{x}\leqslant\frac{\pi}{\mathrm{4}} \\ $$$$\:{then}\:{Df}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{8}}\right)=\frac{{a}}{{b}\sqrt{{b}}}\:{so}\:\begin{cases}{{a}=?}\\{{b}=?}\end{cases} \\ $$

Question Number 160305 Answers: 0 Comments: 0

Question Number 160304 Answers: 0 Comments: 0

Question Number 160136 Answers: 1 Comments: 0

1+4+((16)/2)+((64)/6)+...+(4^n /(n!))=?

$$\mathrm{1}+\mathrm{4}+\frac{\mathrm{16}}{\mathrm{2}}+\frac{\mathrm{64}}{\mathrm{6}}+...+\frac{\mathrm{4}^{{n}} }{{n}!}=? \\ $$

Question Number 159817 Answers: 0 Comments: 0

Question Number 158862 Answers: 1 Comments: 0

Question Number 158805 Answers: 0 Comments: 0

(1)F(x)= x^3 [ x ] ⇒ { ((F ′(0)=?)),((F ′(1)=?)) :} (2) F(x)= [ x ]−∣x∣ ⇒F ′(−(5/2))=? where [ ] : floor function ∣ ∣ absolute function

$$\left(\mathrm{1}\right){F}\left({x}\right)=\:{x}^{\mathrm{3}} \:\left[\:{x}\:\right]\:\Rightarrow\begin{cases}{{F}\:'\left(\mathrm{0}\right)=?}\\{{F}\:'\left(\mathrm{1}\right)=?}\end{cases} \\ $$$$\:\left(\mathrm{2}\right)\:{F}\left({x}\right)=\:\left[\:{x}\:\right]−\mid{x}\mid\:\Rightarrow{F}\:'\left(−\frac{\mathrm{5}}{\mathrm{2}}\right)=? \\ $$$$\:{where}\:\left[\:\right]\::\:{floor}\:{function} \\ $$$$\:\mid\:\mid\:{absolute}\:{function}\: \\ $$

Question Number 158668 Answers: 1 Comments: 0

f(f(x))= (9x^2 +6x+2)f(x) f(x)=?

$$\:{f}\left({f}\left({x}\right)\right)=\:\left(\mathrm{9}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{2}\right){f}\left({x}\right) \\ $$$$\:{f}\left({x}\right)=? \\ $$

Question Number 158334 Answers: 1 Comments: 3

lim_(x→∞) (1/x)Σ_(r=1) ^x cos(((rπ)/(2x))) x∈N

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\underset{{r}=\mathrm{1}} {\overset{{x}} {\sum}}{cos}\left(\frac{{r}\pi}{\mathrm{2}{x}}\right) \\ $$$${x}\in\mathbb{N} \\ $$

Question Number 158306 Answers: 0 Comments: 3

Question Number 158166 Answers: 0 Comments: 1

If f((x/3))=((f(x))/2) and f(1−x)=1−f(x). find f(((173)/(1993))).

$$\:{If}\:{f}\left(\frac{{x}}{\mathrm{3}}\right)=\frac{{f}\left({x}\right)}{\mathrm{2}}\:{and}\:{f}\left(\mathrm{1}−{x}\right)=\mathrm{1}−{f}\left({x}\right). \\ $$$${find}\:{f}\left(\frac{\mathrm{173}}{\mathrm{1993}}\right). \\ $$

Question Number 156793 Answers: 1 Comments: 0

∫_0 ^( (π/2)) ((sin2x)/(2−sin^2 2x))dx

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{sin}\mathrm{2}{x}}{\mathrm{2}−{sin}^{\mathrm{2}} \mathrm{2}{x}}{dx} \\ $$

Question Number 156647 Answers: 0 Comments: 0

Question Number 155809 Answers: 1 Comments: 0

Given that f○g = (x^2 /(2x^2 − x + 4)) and g(x) = (x/(x − 2)), find f(x) ?

$$\:\:\mathrm{Given}\:\mathrm{that}\:{f}\circ{g}\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{4}}\:\:\mathrm{and} \\ $$$$\:\:{g}\left({x}\right)\:=\:\frac{{x}}{{x}\:−\:\mathrm{2}},\:\mathrm{find}\:{f}\left({x}\right)\:? \\ $$$$ \\ $$

Question Number 154668 Answers: 1 Comments: 2

If f(x)=f(x−1)+f(x+1) where f(10)=6 and f(20)=2f(21) then f(16)=…?

$$\:{If}\:{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)\:{where} \\ $$$${f}\left(\mathrm{10}\right)=\mathrm{6}\:{and}\:{f}\left(\mathrm{20}\right)=\mathrm{2}{f}\left(\mathrm{21}\right) \\ $$$${then}\:{f}\left(\mathrm{16}\right)=\ldots? \\ $$

Question Number 154553 Answers: 0 Comments: 0

Π_(n=1) ^∞ (( Γ(n+ (1/n^2 )) )/( Γ(n+ (1/n)) ))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\:\Gamma\left({n}+\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:}{\:\Gamma\left({n}+\:\frac{\mathrm{1}}{{n}}\right)\:} \\ $$$$\: \\ $$

Question Number 154467 Answers: 1 Comments: 0

Π_(n=1) ^∞ (((1+ (1/n))^(1/2) )/(1+ (1/(2n))))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2}{n}}} \\ $$$$\: \\ $$

Question Number 154441 Answers: 1 Comments: 1

Π_(n=1) ^∞ (( (1+ (1/n))^2 )/( 1+ (2/n) ))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\:\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} \:}{\:\mathrm{1}+\:\frac{\mathrm{2}}{{n}}\:} \\ $$$$\: \\ $$

Question Number 153915 Answers: 1 Comments: 0

Question Number 153679 Answers: 1 Comments: 0

Find the constant of polynom P(11x−2) if given the equation 3P(x+2)−P(2x+3)=−4x^2 −x+3

$${Find}\:{the}\:{constant}\:{of}\:{polynom} \\ $$$$\:{P}\left(\mathrm{11}{x}−\mathrm{2}\right)\:{if}\:{given}\:{the}\:{equation} \\ $$$$\mathrm{3}{P}\left({x}+\mathrm{2}\right)−{P}\left(\mathrm{2}{x}+\mathrm{3}\right)=−\mathrm{4}{x}^{\mathrm{2}} −{x}+\mathrm{3} \\ $$

Question Number 152799 Answers: 1 Comments: 1

Given that f○g = (x^2 /(2x^2 − x + 4)) and g(x) = (x/(x − 2)), find f(x).

Question Number 152769 Answers: 1 Comments: 1

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