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why can′t we differentiate or intergrate powers of trigonometric functions such as 1) ∫cos^2 xdx? 3) ∫tan^2 2xdx 2)∫sin^2 xdx? 4) ∫sin^(10) x hence how do we solve such problems.?

$${why}\:{can}'{t}\:{we}\:{differentiate}\:{or}\:{intergrate}\:{powers}\:{of}\:{trigonometric} \\ $$$${functions}\:{such}\:{as}\: \\ $$$$\left.\mathrm{1}\left.\right)\:\int{cos}^{\mathrm{2}} {xdx}?\:\:\:\:\mathrm{3}\right)\:\int{tan}^{\mathrm{2}} \mathrm{2}{xdx} \\ $$$$\left.\mathrm{2}\left.\right)\int{sin}^{\mathrm{2}} {xdx}?\:\:\:\:\:\mathrm{4}\right)\:\int{sin}^{\mathrm{10}} {x} \\ $$$${hence}\:{how}\:{do}\:{we}\:{solve}\:{such}\:{problems}.? \\ $$

Question Number 64015 Answers: 1 Comments: 0

How can such questions be solved.? x^2 −∣7∣ +10=0 x^2 −∣x∣−6>0

$$\:{How}\:{can}\:{such}\:{questions}\:{be}\:{solved}.? \\ $$$$\:\:{x}^{\mathrm{2}} −\mid\mathrm{7}\mid\:+\mathrm{10}=\mathrm{0} \\ $$$$\:\:{x}^{\mathrm{2}} −\mid{x}\mid−\mathrm{6}>\mathrm{0} \\ $$$$\:\: \\ $$

Question Number 63984 Answers: 1 Comments: 5

is it true? e^(lnx) = x? if so then (d/dx)(e^(lnx) )=?

$${is}\:{it}\:{true}? \\ $$$$\:\:{e}^{{lnx}} =\:{x}? \\ $$$${if}\:{so}\:{then}\:\:\frac{{d}}{{dx}}\left({e}^{{lnx}} \right)=? \\ $$

Question Number 63983 Answers: 1 Comments: 0

Please i need someones help on this How do i find an Asymptote to a curve? and also how find a general solution for a differential equation.

$${Please}\:{i}\:{need}\:{someones}\:{help}\:{on}\:{this}\: \\ $$$${How}\:{do}\:{i}\:{find}\:{an}\:{Asymptote}\:{to}\:{a}\:{curve}? \\ $$$${and}\:{also}\:{how}\:{find}\:{a}\:{general}\:{solution}\:{for}\:{a}\:{differential}\: \\ $$$${equation}. \\ $$$$ \\ $$

Question Number 63891 Answers: 0 Comments: 0

A bus is travelling along a straight road at 100Km/hr and the bus conductor walks at 6Km/hr on the floor of the bus and in the same direction as the bus. Find the speed of the conductor relative to the road, and relative to the bus. If the bus conductor now works at the same rate but in the opposite direction as the bus, find his new speed relative to the road. Answers in textbook: 106Km/hr, 64Km/hr, 94Km/hr

Question Number 63812 Answers: 0 Comments: 2

A can terminate a work 9 hour earlier than B. A and B terminate that work after 20 hour together. A can terminate that work after .... hour.

$$ \\ $$$${A}\:\:{can}\:{terminate}\:{a}\:{work}\:\:\mathrm{9}\:{hour}\:{earlier} \\ $$$${than}\:{B}. \\ $$$${A}\:\:{and}\:\:{B}\:\:{terminate}\:{that}\:{work}\:\:{after}\:\mathrm{20}\:{hour}\:{together}. \\ $$$${A}\:{can}\:{terminate}\:{that}\:{work}\:{after}\:....\:{hour}. \\ $$$$ \\ $$$$ \\ $$

Question Number 63758 Answers: 0 Comments: 6

Tanmay Sir. Are you ok ?

$$\mathrm{Tanmay}\:\mathrm{Sir}.\:\mathrm{Are}\:\mathrm{you}\:\mathrm{ok}\:? \\ $$

Question Number 63790 Answers: 2 Comments: 0

Question Number 63789 Answers: 0 Comments: 0

Question Number 63788 Answers: 1 Comments: 0

Question Number 63700 Answers: 0 Comments: 0

Question Number 63689 Answers: 0 Comments: 3

Show that if a∣b then an∣bn

$${Show}\:{that}\:\:{if}\:\:{a}\mid{b}\:\:{then}\:{an}\mid{bn} \\ $$

Question Number 63684 Answers: 0 Comments: 0

cot 118

$$\mathrm{cot}\:\mathrm{118} \\ $$

Question Number 63552 Answers: 1 Comments: 1

Calculate ∫_0 ^(1/2) x(√(x^2 +1)) dx+∫_(1/2) ^1 x^2 (√(x^3 +1)) dx+∫_1 ^2 x^3 (√(x^4 +1)) dx+∫_2 ^3 x^4 (√(x^5 +1 ))dx+...+∫_(78) ^(79) x^(80) (√(x^(81) +1)) dx+∫_(79) ^(80) x^(81) (√(x^(82) +1)) dx usingΣ_(n=2) ^(80) ∫_(n−1) ^n x^(n+1) (√(x^(n+2) +1))dx

$${Calculate}\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}+\underset{\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}+\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx}+\underset{\mathrm{2}} {\overset{\mathrm{3}} {\int}}{x}^{\mathrm{4}} \sqrt{{x}^{\mathrm{5}} +\mathrm{1}\:}{dx}+...+\underset{\mathrm{78}} {\overset{\mathrm{79}} {\int}}{x}^{\mathrm{80}} \sqrt{{x}^{\mathrm{81}} +\mathrm{1}}\:{dx}+\underset{\mathrm{79}} {\overset{\mathrm{80}} {\int}}{x}^{\mathrm{81}} \sqrt{{x}^{\mathrm{82}} +\mathrm{1}}\:{dx} \\ $$$${using}\underset{{n}=\mathrm{2}} {\overset{\mathrm{80}} {\sum}}\underset{{n}−\mathrm{1}} {\overset{{n}} {\int}}{x}^{{n}+\mathrm{1}} \sqrt{{x}^{{n}+\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 63534 Answers: 1 Comments: 0

find the set of values of x for which y is real if y=(((x−2)(x−1))/(x+2)) , x≠−2, x∈R

$${find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{for}\:{which}\:{y}\:{is}\:{real}\:{if}\: \\ $$$$\:{y}=\frac{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{1}\right)}{{x}+\mathrm{2}}\:,\:{x}\neq−\mathrm{2},\:{x}\in\mathbb{R} \\ $$

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