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Question Number 101110 Answers: 1 Comments: 0

Question Number 101107 Answers: 2 Comments: 2

Question Number 101104 Answers: 2 Comments: 0

(d/dx)(x!)=?

$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}!\right)=? \\ $$

Question Number 101162 Answers: 0 Comments: 6

New version with search option is now live on playstore. 2.087. Search Option: press funnel icon and select search question. While searching type the of expression fully − especially integral and summation. ∫((sinx)/x) will not match with ∫_0 ^∞ ((sin x)/x) ∫(√(tan x))dx will also match with∫(√(tanθ))dθ (a/(b+c)) will also match with (x/(y+z)) etc Reindexing is done once a day so question posted recently will not show in search results.

$$\mathrm{New}\:\mathrm{version}\:\mathrm{with}\:\mathrm{search}\:\mathrm{option} \\ $$$$\mathrm{is}\:\mathrm{now}\:\mathrm{live}\:\mathrm{on}\:\mathrm{playstore}.\:\mathrm{2}.\mathrm{087}. \\ $$$$\mathrm{Search}\:\mathrm{Option}: \\ $$$$\mathrm{press}\:\mathrm{funnel}\:\mathrm{icon}\:\mathrm{and}\:\mathrm{select}\:\mathrm{search} \\ $$$$\mathrm{question}. \\ $$$$\mathrm{While}\:\mathrm{searching}\:\mathrm{type}\:\mathrm{the}\: \\ $$$$\mathrm{of}\:\mathrm{expression}\:\mathrm{fully}\:−\:\mathrm{especially} \\ $$$$\mathrm{integral}\:\mathrm{and}\:\mathrm{summation}. \\ $$$$\int\frac{\mathrm{sinx}}{\mathrm{x}}\:\mathrm{will}\:\mathrm{not}\:\mathrm{match}\:\mathrm{with}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:{x}}{{x}} \\ $$$$\int\sqrt{\mathrm{tan}\:{x}}{dx}\:\mathrm{will}\:\mathrm{also}\:\mathrm{match}\:\mathrm{with}\int\sqrt{\mathrm{tan}\theta}{d}\theta \\ $$$$\frac{{a}}{{b}+{c}}\:\mathrm{will}\:\mathrm{also}\:\mathrm{match}\:\mathrm{with}\:\frac{{x}}{{y}+{z}}\:\mathrm{etc} \\ $$$$ \\ $$$$\mathrm{Reindexing}\:\mathrm{is}\:\mathrm{done}\:\mathrm{once}\:\mathrm{a}\:\mathrm{day}\:\mathrm{so} \\ $$$$\mathrm{question}\:\mathrm{posted}\:\mathrm{recently}\:\mathrm{will}\:\mathrm{not} \\ $$$$\mathrm{show}\:\mathrm{in}\:\mathrm{search}\:\mathrm{results}. \\ $$

Question Number 101096 Answers: 1 Comments: 2

find the oblique asymptote of f(x)=x∙e^(1/x) i need your help

$$\mathrm{find}\:\mathrm{the}\:\mathrm{oblique}\:\mathrm{asymptote}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\centerdot\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \:\:\:\:\: \\ $$$$\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help} \\ $$

Question Number 101085 Answers: 1 Comments: 1

Question Number 101073 Answers: 1 Comments: 0

∫_0 ^∞ ((sin(logx))/(logx))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({logx}\right)}{{logx}}{dx} \\ $$

Question Number 101062 Answers: 1 Comments: 0

Question Number 101057 Answers: 1 Comments: 0

Find the area bounded the curves f(x)= ∣x^3 −4x^2 +3x∣ and x−axis

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{the}\: \\ $$$$\mathrm{curves}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mid{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}{x}\mid\:\mathrm{and}\: \\ $$$$\mathrm{x}−\mathrm{axis}\: \\ $$

Question Number 101056 Answers: 5 Comments: 1

If the equation 4x^2 −4(5x+1)+p^2 =0 has one root equals to two more then the other, then the value of p is equal to ___

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}\left(\mathrm{5}{x}+\mathrm{1}\right)+{p}^{\mathrm{2}} =\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equals}\:\mathrm{to}\:\mathrm{two}\:\mathrm{more} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{other},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_ \\ $$

Question Number 101052 Answers: 2 Comments: 0

Given a=^3 (√(7+(√(50)))),b=^3 (√(7−(√(50)))).Prove that a^7 +b^7 is an even number.

$$\mathrm{Given}\:\mathrm{a}=\:^{\mathrm{3}} \sqrt{\mathrm{7}+\sqrt{\mathrm{50}}},\mathrm{b}=\:^{\mathrm{3}} \sqrt{\mathrm{7}−\sqrt{\mathrm{50}}}.\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{7}} +\mathrm{b}^{\mathrm{7}} \mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{number}. \\ $$

Question Number 101051 Answers: 1 Comments: 1

Question Number 101046 Answers: 0 Comments: 1

A new enhacement has been implemented to search already posted question in forum. Press funnel icon while in forum. Editor will open. Type search text say ∫(√(tan x))dx etc press send button.

$$\mathrm{A}\:\mathrm{new}\:\mathrm{enhacement}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{implemented}\:\mathrm{to}\:\mathrm{search}\:\mathrm{already} \\ $$$$\mathrm{posted}\:\mathrm{question}\:\mathrm{in}\:\mathrm{forum}. \\ $$$$\mathrm{Press}\:\mathrm{funnel}\:\mathrm{icon}\:\mathrm{while}\:\mathrm{in}\:\mathrm{forum}. \\ $$$$\mathrm{Editor}\:\mathrm{will}\:\mathrm{open}. \\ $$$$\mathrm{Type}\:\mathrm{search}\:\mathrm{text}\:\mathrm{say}\:\int\sqrt{\mathrm{tan}\:{x}}{dx}\:{etc} \\ $$$$\mathrm{press}\:\mathrm{send}\:\mathrm{button}. \\ $$

Question Number 101043 Answers: 1 Comments: 0

((1+(1/2^(11) ) +(1/3^(11) ) +(1/4^(11) ) + ...)/(1−(1/2^(11) )+(1/3^(11) )−(1/4^(11) )+...)) =?

$$\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{11}} }\:+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{11}} }\:+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{11}} }\:+\:...}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{11}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{11}} }−\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{11}} }+...}\:=? \\ $$

Question Number 101040 Answers: 1 Comments: 0

Express 2 sin θ cos 6θ in the form sin A − sin B (i) using that result prove that 2sin θ( cos 6θ + cos 4θ + cos 2θ) = sin 7θ−sin θ (ii) deduce the result cos (((12π)/7)) + cos (((8π)/7)) + cos (((4π)/7)) = −(1/2) (iii) hence find a general solution to ((sin7θ − sin θ)/(cos 6θ + cos 4θ + cos 2θ)) = 1

$$\:\mathrm{Express}\:\mathrm{2}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\mathrm{6}\theta\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\mathrm{sin}\:{A}\:−\:\mathrm{sin}\:{B} \\ $$$$\left({i}\right)\:\mathrm{using}\:\mathrm{that}\:\mathrm{result}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{2sin}\:\theta\left(\:\mathrm{cos}\:\mathrm{6}\theta\:+\:\mathrm{cos}\:\mathrm{4}\theta\:+\:\mathrm{cos}\:\mathrm{2}\theta\right)\:=\:\mathrm{sin}\:\mathrm{7}\theta−\mathrm{sin}\:\theta \\ $$$$\left({ii}\right)\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{result}\:\mathrm{cos}\:\left(\frac{\mathrm{12}\pi}{\mathrm{7}}\right)\:+\:\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{7}}\right)\:+\:\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{7}}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({iii}\right)\:\mathrm{hence}\:\mathrm{find}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\frac{\mathrm{sin7}\theta\:−\:\mathrm{sin}\:\theta}{\mathrm{cos}\:\mathrm{6}\theta\:+\:\mathrm{cos}\:\mathrm{4}\theta\:+\:\mathrm{cos}\:\mathrm{2}\theta}\:=\:\mathrm{1} \\ $$

Question Number 101079 Answers: 2 Comments: 2

Question Number 101082 Answers: 0 Comments: 2

The value of e^(log_(10) tan 1°+log_(10) tan 2°+log_(10) tan 3°+...+log_(10) tan 89°) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$${e}^{\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{1}°+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{2}°+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{3}°+...+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{89}°} \\ $$$$\mathrm{is} \\ $$

Question Number 101078 Answers: 1 Comments: 0

find the following sum Σ_(k=1) ^n C_( n) ^( k) x^(−k) (k−1)!

$${find}\:\:{the}\:\:{following}\:\:\:{sum} \\ $$$$\:\:\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{C}_{\:{n}} ^{\:{k}} {x}^{−{k}} \left({k}−\mathrm{1}\right)! \\ $$

Question Number 101026 Answers: 1 Comments: 0

lim_(x→∞) (x/e^( sinx −x) )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}}{{e}^{\:\mathrm{sin}{x}\:−{x}} } \\ $$

Question Number 101023 Answers: 0 Comments: 0

∫tan^(1/5) x cotx secxdx

$$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {x}\:{cotx}\:{secxdx} \\ $$

Question Number 101014 Answers: 0 Comments: 0

Show that ∫_(−∞) ^(+∞) (dx/(1+(x+tanx)^2 )) = π

$${Show}\:{that} \\ $$$$\int_{−\infty} ^{+\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tanx}\right)^{\mathrm{2}} }\:\:\:=\:\:\:\pi \\ $$

Question Number 101011 Answers: 0 Comments: 5

∫_0 ^∞ ((sinx)/x)dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}}{dx} \\ $$

Question Number 101008 Answers: 1 Comments: 0

Given f(x) = { (((1/2)xe^(1/x) , x ≠ 0)),((0, x = 0 )) :} find (i) Thd domain of f (ii) check the continuity of f at x = 0 (iii) check its differentiability and its sign (i) sketch this curve and find lim_(x→−∞) f(x) and lim_(x→+∞) f(x)

$$\mathrm{Given}\:{f}\left({x}\right)\:=\:\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}}{xe}^{\frac{\mathrm{1}}{{x}}} \:,\:{x}\:\neq\:\mathrm{0}}\\{\mathrm{0},\:{x}\:=\:\mathrm{0}\:}\end{cases} \\ $$$$\mathrm{find} \\ $$$$\left({i}\right)\:\mathrm{Thd}\:\mathrm{domain}\:\mathrm{of}\:{f} \\ $$$$\left({ii}\right)\:\mathrm{check}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{of}\:{f}\:\mathrm{at}\:{x}\:=\:\mathrm{0} \\ $$$$\left({iii}\right)\:\mathrm{check}\:\mathrm{its}\:\mathrm{differentiability}\:\mathrm{and}\:\mathrm{its}\:\mathrm{sign} \\ $$$$\left({i}\right)\:\mathrm{sketch}\:\mathrm{this}\:\mathrm{curve}\:\mathrm{and}\:\mathrm{find}\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{and}\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$

Question Number 101018 Answers: 0 Comments: 0

∫_(−∞) ^∞ ((log(sin^2 x))/(1+x+e^x ))dx

$$\int_{−\infty} ^{\infty} \frac{{log}\left({sin}^{\mathrm{2}} {x}\right)}{\mathrm{1}+{x}+{e}^{{x}} }{dx} \\ $$

Question Number 101003 Answers: 0 Comments: 0

What is the value of x for wich the serie is converge? (1) Σ_(n≥0) x^((ln(n))/(n!)) ? (2) Σ_(n≥0 ) x^((ln(n!))/n) ?

$$\:\boldsymbol{{What}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{wich}}\:\boldsymbol{{the}}\:\boldsymbol{{serie}}\:\boldsymbol{{is}}\:\boldsymbol{{converge}}?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\left(\mathrm{1}\right)\:\underset{\boldsymbol{{n}}\geqslant\mathrm{0}} {\sum}\boldsymbol{{x}}^{\frac{\boldsymbol{{ln}}\left(\boldsymbol{{n}}\right)}{\boldsymbol{{n}}!}} \:?\:\:\:\:\:\:\left(\mathrm{2}\right)\:\underset{\boldsymbol{{n}}\geqslant\mathrm{0}\:} {\sum}\boldsymbol{{x}}^{\frac{\boldsymbol{{ln}}\left(\boldsymbol{{n}}!\right)}{\boldsymbol{{n}}}} \:? \\ $$$$ \\ $$

Question Number 101001 Answers: 1 Comments: 0

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