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Question Number 60386 Answers: 1 Comments: 4

lim_(x→0) ((sin(πcos^2 x))/x^2 ) why it can not be solved this way lim_(x→0) ((sin(πcos^2 x))/x^2 ) =lim_(x→0) ((sin(πcos^2 x))/(πcos^2 x))×lim_(x→0) ((πcos^2 x)/x^2 ) =π × lim_(x→0) ((cos^2 x)/x^2 ) but it is not equal to π

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$${why}\:{it}\:{can}\:{not}\:{be}\:{solved}\:{this}\:{way} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{\pi{cos}^{\mathrm{2}} {x}}×\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\pi{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$$=\pi\:×\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$${but}\:{it}\:{is}\:{not}\:{equal}\:{to}\:\pi \\ $$

Question Number 60384 Answers: 0 Comments: 0

∫e^(coth^(−1) (x)) dx

$$\int{e}^{{coth}^{−\mathrm{1}} \left({x}\right)} \:{dx}\: \\ $$

Question Number 60376 Answers: 1 Comments: 2

Question Number 60370 Answers: 2 Comments: 0

Question Number 60367 Answers: 0 Comments: 6

Question Number 60362 Answers: 0 Comments: 1

Question Number 60340 Answers: 0 Comments: 0

Question Number 60337 Answers: 0 Comments: 2

15,25,42,...?

$$\mathrm{15},\mathrm{25},\mathrm{42},...? \\ $$

Question Number 60335 Answers: 0 Comments: 0

find I_n = ∫ x^n arctan(x)dx with n integr natural.

$${find}\:{I}_{{n}} =\:\int\:\:{x}^{{n}} \:{arctan}\left({x}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$

Question Number 60330 Answers: 0 Comments: 1

Question Number 60354 Answers: 0 Comments: 0

Question Number 60351 Answers: 0 Comments: 2

Question Number 60357 Answers: 0 Comments: 1

Question Number 60347 Answers: 1 Comments: 1

Question Number 60346 Answers: 0 Comments: 1

∫xsec^3 xdx please help

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$$${please}\:{help} \\ $$

Question Number 60322 Answers: 1 Comments: 2

Question Number 60321 Answers: 0 Comments: 2

Question Number 60320 Answers: 0 Comments: 1

Question Number 60319 Answers: 0 Comments: 0

Question Number 60318 Answers: 0 Comments: 2

Question Number 60439 Answers: 2 Comments: 1

Question Number 60313 Answers: 3 Comments: 1

Question Number 60311 Answers: 1 Comments: 2

∫(dx/(√(sec h^2 (x)+1))) dx

$$\int\frac{{dx}}{\sqrt{{sec}\:{h}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}}\:{dx} \\ $$

Question Number 60308 Answers: 0 Comments: 0

Question Number 60307 Answers: 0 Comments: 0

Question Number 60304 Answers: 0 Comments: 0

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