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Question Number 85930 Answers: 0 Comments: 1

Question Number 85915 Answers: 1 Comments: 0

3^(^(∣x∣) log 27) ≥ ((81)/x)

$$\mathrm{3}^{\:^{\mid\mathrm{x}\mid} \mathrm{log}\:\mathrm{27}} \:\geqslant\:\frac{\mathrm{81}}{\mathrm{x}} \\ $$

Question Number 85914 Answers: 1 Comments: 0

Let I_n =∫_(0 ) ^(π/4) (((1−tan A)/(1+tan A)))^n dA what is the Laplace Transform and the Fourier Transform

$${Let}\:{I}_{{n}} =\overset{\pi/\mathrm{4}} {\int}_{\mathrm{0}\:} \left(\frac{\mathrm{1}−\mathrm{tan}\:{A}}{\mathrm{1}+\mathrm{tan}\:{A}}\right)^{{n}} {dA}\:\:{what}\:{is} \\ $$$${the}\:{Laplace}\:{Transform}\:{and}\:{the} \\ $$$${Fourier}\:{Transform} \\ $$

Question Number 85909 Answers: 2 Comments: 2

∫ sin^(−1) ((√(x/(a+x)))) dx , a > 0

$$\int\:\mathrm{sin}^{−\mathrm{1}} \:\left(\sqrt{\frac{\mathrm{x}}{\mathrm{a}+\mathrm{x}}}\right)\:\mathrm{dx}\:,\:\mathrm{a}\:>\:\mathrm{0} \\ $$

Question Number 85902 Answers: 1 Comments: 15

find the coefficients of x^2 and x^3 terms in the expansion of (1+x)(1+2x)^2 (1+3x)^3 ...(1+100x)^(100)

$${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} ...\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$

Question Number 85896 Answers: 2 Comments: 4

Question Number 85890 Answers: 0 Comments: 0

Is there a sum for ψ((p/q)) or an integral for any fraction p/q

$${Is}\:{there}\:{a}\:{sum}\:{for}\:\psi\left(\frac{{p}}{{q}}\right)\:{or}\:{an}\:{integral} \\ $$$${for}\:{any}\:{fraction}\:{p}/{q} \\ $$

Question Number 85888 Answers: 0 Comments: 5

i−∫_0 ^5 (x+[2x])^([(x/3)]) dx ii−∫_0 ^3 (z−{z})^([z]) dz

$${i}−\int_{\mathrm{0}} ^{\mathrm{5}} \left({x}+\left[\mathrm{2}{x}\right]\right)^{\left[\frac{{x}}{\mathrm{3}}\right]} {dx} \\ $$$$ \\ $$$${ii}−\int_{\mathrm{0}} ^{\mathrm{3}} \left({z}−\left\{{z}\right\}\right)^{\left[{z}\right]} \:{dz} \\ $$

Question Number 85875 Answers: 1 Comments: 0

∫((1/(7[1−(1/7)e^x ]))) dx

$$\int\left(\frac{\mathrm{1}}{\mathrm{7}\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{7}}\mathrm{e}^{\mathrm{x}} \right]}\right)\:\mathrm{dx} \\ $$

Question Number 85872 Answers: 1 Comments: 1

∫cos^(2020) x dx = ?

$$\int\mathrm{cos}^{\mathrm{2020}} \mathrm{x}\:\mathrm{dx}\:=\:? \\ $$

Question Number 85871 Answers: 0 Comments: 3

Question Number 85868 Answers: 0 Comments: 6

if f(x)=⌊x^2 ⌋ and A=lim_(x→0) (f(x)−f(−x)) and B=f(x)+f(−x) when x=0 find A and B

$${if}\:{f}\left({x}\right)=\lfloor{x}^{\mathrm{2}} \rfloor\:\: \\ $$$${and}\:{A}=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left({f}\left({x}\right)−{f}\left(−{x}\right)\right) \\ $$$${and}\:{B}={f}\left({x}\right)+{f}\left(−{x}\right)\:\:{when}\:{x}=\mathrm{0} \\ $$$$ \\ $$$${find}\:{A}\:{and}\:{B} \\ $$

Question Number 85866 Answers: 2 Comments: 1

Question Number 85865 Answers: 1 Comments: 0

prove that curl(r^n c^→ ×r^→ )=(n+2)r^n c^→ −nr^(n−2) (r^→ .c^→ ) . where c is the constant vector.

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{curl}\left(\mathrm{r}^{\mathrm{n}} \overset{\rightarrow} {\mathrm{c}}×\overset{\rightarrow} {\mathrm{r}}\right)=\left(\mathrm{n}+\mathrm{2}\right)\mathrm{r}^{\mathrm{n}} \overset{\rightarrow} {\mathrm{c}}−\mathrm{nr}^{\mathrm{n}−\mathrm{2}} \left(\overset{\rightarrow} {\mathrm{r}}.\overset{\rightarrow} {\mathrm{c}}\right)\:\:. \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{vector}. \\ $$

Question Number 85864 Answers: 1 Comments: 0

simplify the expression (√(6+2(√(8(√3)−10)))) − (√(7−(√3))) in the form (√((√a)+b)) ?

$${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$

Question Number 85859 Answers: 2 Comments: 0

Is the Var(aX+b) = a^2 Var(X) + b?

$$\:\mathrm{Is}\:\mathrm{the}\:\mathrm{Var}\left(\mathrm{aX}+\mathrm{b}\right)\:=\:\mathrm{a}^{\mathrm{2}} \:\mathrm{Var}\left(\mathrm{X}\right)\:+\:\mathrm{b}? \\ $$

Question Number 85858 Answers: 0 Comments: 0

Is a matrix A^T A always positive definite?

$$\mathrm{Is}\:\mathrm{a}\:\mathrm{matrix} \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{A}\:\mathrm{always}\:\mathrm{positive}\:\mathrm{definite}? \\ $$

Question Number 85857 Answers: 1 Comments: 0

Question Number 85854 Answers: 0 Comments: 2

If x,y,z ∈ R satisfy the equation x^4 + y^4 + z^4 = 4xyz −1 find minimum value of x + y + z

$$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$

Question Number 85846 Answers: 0 Comments: 2

∫_( 0) ^(50π) ∣ cos x ∣dx =

$$\underset{\:\mathrm{0}} {\overset{\mathrm{50}\pi} {\int}}\:\mid\:\mathrm{cos}\:{x}\:\mid{dx}\:= \\ $$

Question Number 85845 Answers: 2 Comments: 0

solve tanh (x) = (1/(cosh (x)))

$$\mathrm{solve}\:\mathrm{tanh}\:\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cosh}\:\left(\mathrm{x}\right)} \\ $$

Question Number 85839 Answers: 1 Comments: 1

∫x×(1/(√(x^2 −1)))dx

$$\int\mathrm{x}×\frac{\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\mathrm{dx} \\ $$

Question Number 85835 Answers: 1 Comments: 0

xydy=(y^2 +x)dx

$$\mathrm{xydy}=\left(\mathrm{y}^{\mathrm{2}} +\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 85834 Answers: 1 Comments: 0

2y^′ −(x/y)=((xy)/(x^2 −1))

$$\mathrm{2y}^{'} −\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 85832 Answers: 1 Comments: 1

(x+x^(−1) )^2 +(x^2 +x^(−2) )^2 +(x^3 +x^(−3) )^2 + ... + (x^(10) +x^(−10) )^2 =

$$\left(\mathrm{x}+\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{2}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{−\mathrm{3}} \right)^{\mathrm{2}} \\ $$$$+\:...\:+\:\left(\mathrm{x}^{\mathrm{10}} +\mathrm{x}^{−\mathrm{10}} \right)^{\mathrm{2}} \:=\: \\ $$

Question Number 85828 Answers: 1 Comments: 0

∫(1/(x+cot(x))) dx

$$\int\frac{\mathrm{1}}{{x}+{cot}\left({x}\right)}\:{dx} \\ $$

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