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AllQuestion and Answers: Page 177

Question Number 204441 Answers: 0 Comments: 2

Question Number 204437 Answers: 1 Comments: 0

∫_0 ^(Π/2) sin(t)ln(sint)dt

$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} {sin}\left({t}\right){ln}\left({sint}\right){dt} \\ $$

Question Number 204436 Answers: 0 Comments: 0

Question Number 204433 Answers: 3 Comments: 1

Question Number 204428 Answers: 0 Comments: 1

Question Number 204426 Answers: 1 Comments: 0

let a , b >0 find all differentiable function f:(0,∞)→(0,∞) such that f′((a/x)) = ((bx)/(f(x))) , ∀ x>0

$$\:\:\mathrm{let}\:\mathrm{a}\:,\:\mathrm{b}\:>\mathrm{0}\:\:\mathrm{find}\:\mathrm{all}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\:\:\:\mathrm{f}:\left(\mathrm{0},\infty\right)\rightarrow\left(\mathrm{0},\infty\right)\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\mathrm{f}'\left(\frac{{a}}{\mathrm{x}}\right)\:\:=\:\:\frac{\mathrm{bx}}{\mathrm{f}\left(\mathrm{x}\right)}\:\:\:\:,\:\:\:\forall\:\mathrm{x}>\mathrm{0} \\ $$

Question Number 204461 Answers: 2 Comments: 0

Solve for x (x − 12)(x − 13) = ((34)/(33^2 ))

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\left({x}\:−\:\mathrm{12}\right)\left({x}\:−\:\mathrm{13}\right)\:=\:\frac{\mathrm{34}}{\mathrm{33}^{\mathrm{2}} } \\ $$

Question Number 204423 Answers: 3 Comments: 1

Question Number 204421 Answers: 3 Comments: 0

x^3 +y^3 = 35 (1/x)+(1/y) =(5/6) solve for all possible values of x and y

$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:=\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${solve}\:{for}\:{all}\:{possible}\:{values}\:{of}\:{x}\:{and}\:{y} \\ $$$$ \\ $$

Question Number 204418 Answers: 1 Comments: 1

Question Number 204417 Answers: 2 Comments: 0

Solve for z∈C e^z =ln z

$$\mathrm{Solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{e}^{{z}} =\mathrm{ln}\:{z} \\ $$

Question Number 204410 Answers: 0 Comments: 0

Question Number 204409 Answers: 3 Comments: 1

find ⌊∫_0 ^(2023) (2/(x+e^x ))dx⌋=?

$${find}\:\lfloor\int_{\mathrm{0}} ^{\mathrm{2023}} \frac{\mathrm{2}}{{x}+{e}^{{x}} }{dx}\rfloor=? \\ $$

Question Number 204405 Answers: 1 Comments: 1

Question Number 204398 Answers: 0 Comments: 0

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Question Number 204397 Answers: 3 Comments: 0

Question Number 204396 Answers: 1 Comments: 0

Question Number 204395 Answers: 1 Comments: 0

Question Number 204394 Answers: 0 Comments: 0

Question Number 204393 Answers: 0 Comments: 0

Question Number 204389 Answers: 1 Comments: 0

Question Number 204374 Answers: 0 Comments: 1

Question Number 204373 Answers: 1 Comments: 0

3^x −2^x =65 x=?

$$\mathrm{3}^{{x}} −\mathrm{2}^{{x}} =\mathrm{65} \\ $$$${x}=? \\ $$

Question Number 204372 Answers: 2 Comments: 0

If , f : [ 0 , b] →^(continuous) R , g : R →_(b−periodic) ^(continuous) R ⇒ lim_(n→∞) ∫_0 ^( b) f(x)g(nx)dx=^? (1/b) ∫_0 ^( b) f(x)dx .∫_0 ^( b) g(x)dx

$$ \\ $$$$\:\:{If}\:,\:\:\:\:{f}\::\:\left[\:\mathrm{0}\:,\:{b}\right]\:\overset{{continuous}} {\rightarrow}\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:\:,\:\:\:\:{g}\::\:\mathbb{R}\:\underset{{b}−{periodic}} {\overset{{continuous}} {\rightarrow}}\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){g}\left({nx}\right){dx}\overset{?} {=}\frac{\mathrm{1}}{{b}}\:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){dx}\:.\int_{\mathrm{0}} ^{\:{b}} {g}\left({x}\right){dx} \\ $$$$ \\ $$

Question Number 204384 Answers: 0 Comments: 1

Question Number 204360 Answers: 3 Comments: 0

if lim_(x→+∞) [(((a+6)x+1)/(ax+1))]=2→ find the largest and smallest correct value for a.

$${if} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left[\frac{\left({a}+\mathrm{6}\right){x}+\mathrm{1}}{{ax}+\mathrm{1}}\right]=\mathrm{2}\rightarrow \\ $$$${find}\:{the}\:{largest}\:{and}\:{smallest}\:{correct} \\ $$$${value}\:{for}\:{a}. \\ $$

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