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Question Number 222830 Answers: 1 Comments: 0

Question Number 222829 Answers: 1 Comments: 0

If f(x) = ((3x + [x])/(2x)) Find lim_(x→−5^+ ) f(x) − lim_(x→−5^− ) f(x) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\left[\mathrm{x}\right]}{\mathrm{2x}} \\ $$$$\mathrm{Find}\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{+} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:−\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 222828 Answers: 0 Comments: 0

if vector field is A^→ and F^→ ;R^3 →R^3 A^→ =▽^→ ×F^→ can we find (▽_ ^→ ×)^(−1) and..inverse of div operator (▽_ ^→ ∗)^(−1) ...?? ex. ( ((d )/dx))^(−1) =∫

$$\mathrm{if}\:\mathrm{vector}\:\mathrm{field}\:\mathrm{is}\:\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}\:\mathrm{and}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}=\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}} \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{find} \\ $$$$\left(\overset{\rightarrow} {\bigtriangledown}_{\:} ×\right)^{−\mathrm{1}} \:\mathrm{and}..\mathrm{inverse}\:\mathrm{of}\:\mathrm{div}\:\mathrm{operator}\:\left(\overset{\rightarrow} {\bigtriangledown}_{\:} \ast\right)^{−\mathrm{1}} ...?? \\ $$$$\mathrm{ex}.\:\left(\:\frac{\mathrm{d}\:\:\:}{\mathrm{d}{x}}\right)^{−\mathrm{1}} =\int\: \\ $$

Question Number 222812 Answers: 1 Comments: 0

Question Number 222811 Answers: 1 Comments: 0

∫_0 ^(1/2) ((ln(2x))/( (√(1−x^2 ))))dx

$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 222805 Answers: 2 Comments: 0

Prove:∫_(−∞) ^∞ J_0 (2x)dx=1

$$\mathrm{Prove}:\int_{−\infty} ^{\infty} {J}_{\mathrm{0}} \left(\mathrm{2}{x}\right){dx}=\mathrm{1} \\ $$

Question Number 222801 Answers: 2 Comments: 0

Question Number 222800 Answers: 1 Comments: 0

Question Number 222799 Answers: 0 Comments: 1

x^x^y =9^(xy) x+y=1

$${x}^{{x}^{{y}} } =\mathrm{9}^{{xy}} \\ $$$${x}+{y}=\mathrm{1} \\ $$

Question Number 222798 Answers: 1 Comments: 0

Question Number 222794 Answers: 0 Comments: 0

$$\: \\ $$

Question Number 222787 Answers: 1 Comments: 0

∫_1 ^( π/2) ((4^(−x) ∙ e^(tan(x+x^2 )) ∙ ln(1 + x^3 ))/(1 + x)) dx

$$ \\ $$$$\:\:\:\:\:\int_{\mathrm{1}} ^{\:\pi/\mathrm{2}} \:\:\frac{\mathrm{4}^{−{x}} \:\centerdot\:{e}^{\mathrm{tan}\left({x}+{x}^{\mathrm{2}} \right)} \centerdot\:\mathrm{ln}\left(\mathrm{1}\:+\:{x}^{\mathrm{3}} \right)}{\mathrm{1}\:+\:{x}}\:\:\mathrm{d}{x}\:\:\:\:\: \\ $$$$ \\ $$

Question Number 222783 Answers: 1 Comments: 0

$$\:\underbrace{ } \\ $$

Question Number 222781 Answers: 1 Comments: 0

⪸

$$\:\cancel{\underline{\underbrace{\succapprox}}} \\ $$

Question Number 222779 Answers: 1 Comments: 0

Question Number 222778 Answers: 0 Comments: 0

lim_(x→0) ((2log(1+x)−((x(3x+2))/((x+1)^2 )))/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2log}\left(\mathrm{1}+\mathrm{x}\right)−\frac{\mathrm{x}\left(\mathrm{3x}+\mathrm{2}\right)}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 222777 Answers: 1 Comments: 0

Simplify: (((cos214° + i sin146°)∙(cos10° + i sin10°))/((cos66° − i sin246°))) = ?

$$\mathrm{Simplify}: \\ $$$$\frac{\left(\mathrm{cos214}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin146}°\right)\centerdot\left(\mathrm{cos10}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin10}°\right)}{\left(\mathrm{cos66}°\:−\:\boldsymbol{\mathrm{i}}\:\mathrm{sin246}°\right)}\:=\:? \\ $$

Question Number 222760 Answers: 1 Comments: 0

Question Number 222758 Answers: 1 Comments: 1

Question Number 222756 Answers: 1 Comments: 0

lim_(x→0) ((1−(√(cos(x))))/( x−xcos((√x))))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}}{\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{xcos}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)} \\ $$

Question Number 222754 Answers: 1 Comments: 1

Question Number 222753 Answers: 3 Comments: 0

Question Number 222747 Answers: 1 Comments: 1

Question Number 222744 Answers: 0 Comments: 0

Question Number 222743 Answers: 1 Comments: 0

Compare: a = arcctg (√2) b = arccos ((√2)/2) c = arctg (√2)

$$\mathrm{Compare}: \\ $$$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{arcctg}\:\sqrt{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{b}}\:=\:\mathrm{arccos}\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{c}}\:=\:\mathrm{arctg}\:\sqrt{\mathrm{2}} \\ $$

Question Number 222733 Answers: 0 Comments: 0

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