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Question Number 101277 Answers: 2 Comments: 0

∫_0 ^1 (((x−1) dx )/((x+1)ln (x)))

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left({x}−\mathrm{1}\right)\:{dx}\:}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:\left({x}\right)} \\ $$$$ \\ $$

Question Number 101156 Answers: 1 Comments: 0

Find the range of the function: h : x = 2 − x^2 sin(x), x ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\:\:\:\:\:\mathrm{h}\::\:\mathrm{x}\:\:\:=\:\:\mathrm{2}\:\:−\:\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{x}\right),\:\:\:\:\:\:\mathrm{x}\:\:\geqslant\:\:\mathrm{0} \\ $$

Question Number 101212 Answers: 2 Comments: 1

∫e^x sin x dx = −e^x cos x + e^x sin x − ∫ e^x sin x dx

$$\int{e}^{{x}} \mathrm{sin}\:{x}\:{dx}\:=\:−{e}^{{x}} {cos}\:{x}\:+\:{e}^{{x}} \:{sin}\:{x}\:−\:\int\:{e}^{{x}} \:\mathrm{sin}\:\:{x}\:{dx} \\ $$

Question Number 101148 Answers: 0 Comments: 2

lim_(x→0) ((sin (ln (1+x))−ln(1+sin x))/(sin^4 ((x/2)))) =?

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

Question Number 101192 Answers: 1 Comments: 2

∫ (x/(1+sin x)) dx

$$\int\:\frac{{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\: \\ $$

Question Number 101185 Answers: 2 Comments: 0

In an arithmetic progression the sum of the third term and 8th term is 49 and the sum of the 5th and 9th term is 58.Find the first term and the common difference using simultaneous equations.

$${In}\:{an}\:{arithmetic}\:{progression}\:{the}\:{sum}\:{of}\:{the}\:{third}\:{term}\:{and}\:\mathrm{8}{th}\:{term}\:{is}\:\mathrm{49}\:{and}\:{the}\:{sum}\:{of}\:{the}\:\:\mathrm{5}{th}\:{and}\:\mathrm{9}{th}\:{term}\:{is}\:\mathrm{58}.{Find}\:{the}\:{first}\:{term}\:{and}\:{the}\:{common}\:{difference}\:{using}\:{simultaneous}\:{equations}. \\ $$

Question Number 101183 Answers: 1 Comments: 0

Question Number 101182 Answers: 1 Comments: 0

Consider a square − based pyramid with a height of 6x cm and a base length of (2−x)cm. Find maximum value of volume of pyramid.

$$\mathcal{C}\mathrm{onsider}\:\mathrm{a}\:\mathrm{square}\:−\:\mathrm{based} \\ $$$$\mathrm{pyramid}\:\mathrm{with}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{6}{x}\:\mathrm{cm} \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{base}\:\mathrm{length}\:\mathrm{of}\:\left(\mathrm{2}−{x}\right)\mathrm{cm}. \\ $$$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{pyramid}. \\ $$

Question Number 101178 Answers: 2 Comments: 0

∫ ((((√x)−x)^2 )/x^2 ) dx ?

$$\int\:\frac{\left(\sqrt{\mathrm{x}}−\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$

Question Number 101172 Answers: 1 Comments: 0

Find the range of the function: y = 2 − x^2 sin(x), x ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\:\:\:\:\:\:\mathrm{y}\:\:=\:\:\mathrm{2}\:\:−\:\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{x}\right),\:\:\:\:\:\:\mathrm{x}\:\geqslant\:\mathrm{0} \\ $$

Question Number 101159 Answers: 1 Comments: 0

given the complex number z such that z−4i=a+3zi. find the value of a if z is purwly imaginary

$${given}\:{the}\:{complex}\:{number}\:{z}\:{such}\:{that} \\ $$$${z}−\mathrm{4}{i}={a}+\mathrm{3}{zi}.\: \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{if}\:\:{z}\:{is}\:{purwly}\:{imaginary} \\ $$$$ \\ $$

Question Number 101121 Answers: 1 Comments: 0

Two dice are tossed simultaneously. Find the probability of any showing a number greater than five.

$$\mathrm{Two}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{tossed}\:\mathrm{simultaneously}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{any}\:\mathrm{showing} \\ $$$$\mathrm{a}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{five}. \\ $$

Question Number 101116 Answers: 1 Comments: 0

Question Number 101111 Answers: 0 Comments: 0

{_(y−((1/4))Argch(y)+4ln(x)=4) ^(x−((1/3))e^y +(1/4)Argsh(x)=2) calculer (x.y)?

$$\: \\ $$$$\:\left\{_{\boldsymbol{{y}}−\left(\frac{\mathrm{1}}{\mathrm{4}}\right)\boldsymbol{{Argch}}\left(\boldsymbol{{y}}\right)+\mathrm{4}\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right)=\mathrm{4}} ^{\boldsymbol{{x}}−\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\boldsymbol{{e}}^{\boldsymbol{{y}}} +\frac{\mathrm{1}}{\mathrm{4}}\boldsymbol{{Argsh}}\left(\boldsymbol{{x}}\right)=\mathrm{2}} \:\:\right. \\ $$$$\:\:\boldsymbol{{calculer}}\:\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)? \\ $$

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