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Question Number 99707 Answers: 4 Comments: 1

∫_(−∞) ^∞ e^(−x^2 ) dx=?

$$\int_{−\infty} ^{\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=? \\ $$

Question Number 99697 Answers: 2 Comments: 1

lim_(n→∞) Σ_(k=0) ^(2n) (k/(k+n^2 ))

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{2n}} {\sum}}\frac{\mathrm{k}}{\mathrm{k}+\mathrm{n}^{\mathrm{2}} } \\ $$

Question Number 99698 Answers: 0 Comments: 2

Question Number 99685 Answers: 3 Comments: 3

Find the limits when n goes to infinty of the following summation series; a\(1/n^2 )Σ_(k=1) ^n E(kx), x∈R b\Σ_(k=0) ^n ((n),(k) )^(−1)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{when}\:\mathrm{n}\:\mathrm{goes}\:\mathrm{to}\:\mathrm{infinty}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{summation}\:\mathrm{series}; \\ $$$$\mathrm{a}\backslash\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{E}\left(\mathrm{kx}\right),\:\:\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{b}\backslash\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}^{−\mathrm{1}} \\ $$

Question Number 99681 Answers: 1 Comments: 0

Question Number 99680 Answers: 0 Comments: 0

Question Number 99679 Answers: 0 Comments: 1

Question Number 99677 Answers: 0 Comments: 0

Question Number 99676 Answers: 1 Comments: 0

lim_(x→0) ((sin (sin x)−x)/(x(cos (sin x)−1)))??

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}}{\mathrm{x}\left(\mathrm{cos}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{1}\right)}?? \\ $$

Question Number 99670 Answers: 0 Comments: 2

Question Number 99669 Answers: 0 Comments: 0

Question Number 99667 Answers: 0 Comments: 0

State and prove the fundamental theorem of intergral calculus

$$\mathrm{State}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{fundamental}\:\mathrm{theorem} \\ $$$$\mathrm{of}\:\mathrm{intergral}\:\mathrm{calculus} \\ $$

Question Number 99666 Answers: 0 Comments: 0

Question Number 99665 Answers: 0 Comments: 1

Question Number 99661 Answers: 0 Comments: 0

Question Number 99655 Answers: 1 Comments: 1

Question Number 99646 Answers: 2 Comments: 0

use power series solution method to solve the ODE y′′−xy=0

$$\boldsymbol{{use}}\:\boldsymbol{{power}}\:\boldsymbol{{series}}\:\boldsymbol{{solution}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{ODE}} \\ $$$$\boldsymbol{{y}}''−\boldsymbol{{xy}}=\mathrm{0} \\ $$

Question Number 99645 Answers: 1 Comments: 1

If x,y > 0 then ∣(√(xy))−((x+y)/2)∣ + ∣((x+y)/2) + (√(xy)) ∣ =

$${If}\:{x},{y}\:>\:\mathrm{0}\:{then}\:\mid\sqrt{{xy}}−\frac{{x}+{y}}{\mathrm{2}}\mid\:+\:\mid\frac{{x}+{y}}{\mathrm{2}}\:+\:\sqrt{{xy}}\:\mid\:= \\ $$

Question Number 99623 Answers: 1 Comments: 1

obtain the modulus and arguement of (((1−i)^4 )/((2+2(√(3i)^3 ))))

$${obtain}\:{the}\:{modulus}\:{and}\:{arguement}\:{of} \\ $$$$\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} }{\left(\mathrm{2}+\mathrm{2}\sqrt{\left.\mathrm{3}{i}\right)^{\mathrm{3}} }\right.} \\ $$

Question Number 99621 Answers: 2 Comments: 1

6^x =x^(5 ) x=? help me

$$\mathrm{6}^{\mathrm{x}} =\mathrm{x}^{\mathrm{5}\:\:\:\:\:\:\:} \mathrm{x}=?\:\:\:\:\:\:\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 99620 Answers: 1 Comments: 1

If α=((2π)/7) then what is the value of (sinαsin2αsin4α)

$${If}\:\:\alpha=\frac{\mathrm{2}\pi}{\mathrm{7}}\:\:{then}\:{what}\:{is}\:{the}\:{value}\:{of}\:\left({sin}\alpha{sin}\mathrm{2}\alpha{sin}\mathrm{4}\alpha\right) \\ $$

Question Number 99614 Answers: 0 Comments: 1

Question Number 99612 Answers: 0 Comments: 1

Question Number 99606 Answers: 0 Comments: 1

Question Number 99603 Answers: 1 Comments: 2

How many terms in the geometric progression 1, 1.1, 1.21,1.331,... will be needed so that the sum of the first n terms is greather than 20?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{geometric} \\ $$$$\mathrm{progression}\:\mathrm{1},\:\mathrm{1}.\mathrm{1},\:\mathrm{1}.\mathrm{21},\mathrm{1}.\mathrm{331},... \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{needed}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{greather}\:\mathrm{than}\:\mathrm{20}? \\ $$

Question Number 99600 Answers: 1 Comments: 0

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