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Question Number 72441 Answers: 2 Comments: 1

If^n C_(12) =^n C_8 , then n=

$$\mathrm{If}\:^{{n}} {C}_{\mathrm{12}} =\:^{{n}} {C}_{\mathrm{8}} \:,\:\mathrm{then}\:{n}= \\ $$

Question Number 72439 Answers: 0 Comments: 1

Question Number 72438 Answers: 0 Comments: 0

Question Number 72421 Answers: 1 Comments: 0

Question Number 72416 Answers: 0 Comments: 1

Question Number 72414 Answers: 1 Comments: 1

Question Number 72413 Answers: 0 Comments: 0

Question Number 72408 Answers: 1 Comments: 1

Question Number 72401 Answers: 1 Comments: 0

Find the area bounded by one leaf of the rose r = 12cos (3θ).

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:{one}\:{leaf}\:{of} \\ $$$${the}\:{rose}\:{r}\:=\:\mathrm{12cos}\:\left(\mathrm{3}\theta\right). \\ $$

Question Number 72398 Answers: 0 Comments: 4

lim_(x→∞) [x−x^2 ln(1+(1/x))]

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{x}−\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)\right] \\ $$

Question Number 72397 Answers: 0 Comments: 4

find A(x)=∫_0 ^(π/2) ln(1−xsin^2 θ)dθ with ∣x∣<1

$${find}\:{A}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{xsin}^{\mathrm{2}} \theta\right){d}\theta\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 72396 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((1+x^2 )/(2+x^2 +x^4 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 72395 Answers: 0 Comments: 0

find Σ_(k=0) ^n (C_n ^k )^3

$${find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \left({C}_{{n}} ^{{k}} \right)^{\mathrm{3}} \\ $$

Question Number 72394 Answers: 0 Comments: 3

let g(x)=((ln(1+x))/(3+x^2 )) 1) find g^((n)) (x)and g^((n)) (0) 2)developp g at integr serie

$${let}\:{g}\left({x}\right)=\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{3}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right){and}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{g}\:{at}\:{integr}\:{serie} \\ $$

Question Number 72393 Answers: 0 Comments: 0

let f(x) =cos(narccosx) 1)calculate f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie

$${let}\:{f}\left({x}\right)\:={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 72392 Answers: 0 Comments: 1

calculate A_n =∫_0 ^∞ e^(−nx) ln(1+x)dx with n natural ≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} {ln}\left(\mathrm{1}+{x}\right){dx}\:\:{with}\:{n}\:{natural}\:\geqslant\mathrm{1} \\ $$

Question Number 72391 Answers: 0 Comments: 1

calculte ∫_0 ^∞ (((−1)^([x]) )/(4+x^2 ))dx

$${calculte}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 72362 Answers: 1 Comments: 0

Calculate the sides of a triangle knowing the heights h_(a ) =(1/9) h_b =(1/7) and h_c =(1/4)

$${Calculate}\:{the}\:{sides}\:{of}\:{a}\:{triangle} \\ $$$${knowing}\:{the}\:{heights}\:{h}_{\mathrm{a}\:} =\frac{\mathrm{1}}{\mathrm{9}} \\ $$$${h}_{\mathrm{b}} =\frac{\mathrm{1}}{\mathrm{7}}\:{and}\:{h}_{\mathrm{c}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 72462 Answers: 0 Comments: 2

lim_(x→0) ((1−(√(1+4x ))cos(x^2 ))/(x^3 arctan(x^5 )))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{4x}\:}\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \mathrm{arctan}\left(\mathrm{x}^{\mathrm{5}} \right)} \\ $$

Question Number 72346 Answers: 0 Comments: 1

Question Number 72344 Answers: 0 Comments: 3

prove that e^(lnx) = x or a^(log_a x) = x

$${prove}\:{that}\:\:{e}^{{lnx}} \:=\:{x} \\ $$$${or}\:\:{a}^{{log}_{{a}} {x}} \:=\:{x} \\ $$

Question Number 72343 Answers: 0 Comments: 3

given that y = ln ( 1 + cos^2 x) find (dy/(dx )) at the point x = ((3π)/4) and if y =ln(x^2 + 4) find (dy/dx) at x = 1

$${given}\:{that}\:{y}\:=\:{ln}\:\left(\:\mathrm{1}\:+\:{cos}^{\mathrm{2}} {x}\right)\:{find}\:\frac{{dy}}{{dx}\:\:}\:{at}\:{the}\:{point}\:\:{x}\:=\:\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$$${and}\:\:{if}\:\:{y}\:={ln}\left({x}^{\mathrm{2}} \:+\:\mathrm{4}\right)\:{find}\:\:\frac{{dy}}{{dx}}\:{at}\:{x}\:=\:\mathrm{1} \\ $$

Question Number 72339 Answers: 0 Comments: 1

(√(x + (√(4x + (√(16x + ... + (√(4^(2019) x + 3)))))))) = (√x) + 1

$$\sqrt{{x}\:+\:\sqrt{\mathrm{4}{x}\:+\:\sqrt{\mathrm{16}{x}\:+\:...\:+\:\sqrt{\mathrm{4}^{\mathrm{2019}} {x}\:+\:\mathrm{3}}}}}\:\:=\:\:\sqrt{{x}}\:+\:\mathrm{1} \\ $$

Question Number 72337 Answers: 1 Comments: 1

Evaluate ∫_(−5) ^5 ((√(25−x^2 )) ) dx using ⇒ an algebraic method ⇒ Geometrical mehod thanks in advanced great mathematicians

$${Evaluate}\:\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\:\right)\:{dx}\:{using} \\ $$$$\Rightarrow\:{an}\:{algebraic}\:{method} \\ $$$$\Rightarrow\:{Geometrical}\:{mehod}\: \\ $$$${thanks}\:{in}\:{advanced}\:{great}\:{mathematicians} \\ $$

Question Number 72336 Answers: 0 Comments: 0

Obain an equation for ⇒ the left Reimen Sum ⇒ the right Reimen sum ⇒ Trapeziodal rule ⇒ Newton Raphson′s Iteration Hence find and approximate value for ∫_0 ^3 (e^x + x^2 )dx

$${Obain}\:{an}\:{equation}\:{for}\: \\ $$$$\Rightarrow\:{the}\:{left}\:{Reimen}\:{Sum} \\ $$$$\Rightarrow\:{the}\:{right}\:{Reimen}\:{sum} \\ $$$$\Rightarrow\:{Trapeziodal}\:{rule} \\ $$$$\Rightarrow\:{Newton}\:{Raphson}'{s}\:{Iteration} \\ $$$$\:\:{Hence}\:{find}\:{and}\:{approximate}\:{value}\:{for}\:\int_{\mathrm{0}} ^{\mathrm{3}} \left({e}^{{x}} \:+\:{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 72332 Answers: 1 Comments: 0

let Q=((1+tan(((3π)/8)) . tan((π/(10))))/(1−tan((π/8)).tan((π/(10))))) prove that ((Q−1)/(Q+1))=(√(7−3(√5)−(√(85−38(√5)))))

$${let}\:{Q}=\frac{\mathrm{1}+{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:.\:{tan}\left(\frac{\pi}{\mathrm{10}}\right)}{\mathrm{1}−{tan}\left(\frac{\pi}{\mathrm{8}}\right).{tan}\left(\frac{\pi}{\mathrm{10}}\right)} \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$\: \\ $$$$\frac{{Q}−\mathrm{1}}{{Q}+\mathrm{1}}=\sqrt{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}−\sqrt{\mathrm{85}−\mathrm{38}\sqrt{\mathrm{5}}}} \\ $$$$ \\ $$

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