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Question Number 102763 Answers: 0 Comments: 0

Show that the function defined within [0,1] by f(x)= { ((1 if x∈Q∩[0,1])),((0 otherwise)) :} is not Riemann integrable within [0,1]

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defined}\:\mathrm{within}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{by}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{1}\:\mathrm{if}\:\mathrm{x}\in\mathbb{Q}\cap\left[\mathrm{0},\mathrm{1}\right]}\\{\mathrm{0}\:\mathrm{otherwise}}\end{cases}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{Riemann}\:\mathrm{integrable} \\ $$$$\mathrm{within}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 102753 Answers: 1 Comments: 0

A wedge has a weight of 9kg . And a block has a weight of 2kg If the block starts sliding with an angle of 45° with the horizontal then what is accelaration of the wedge?

$${A}\:{wedge}\:{has}\:{a}\:{weight}\:{of}\:\mathrm{9}{kg}\:.\:{And}\:{a}\:{block}\:{has}\:{a}\:{weight}\:{of}\:\mathrm{2}{kg} \\ $$$${If}\:{the}\:{block}\:{starts}\:{sliding}\:{with}\:{an}\:{angle}\:{of}\:\mathrm{45}°\:{with}\:{the} \\ $$$${horizontal}\:{then}\:{what}\:{is}\:{accelaration}\:{of}\:{the}\:{wedge}? \\ $$$$ \\ $$$$ \\ $$

Question Number 102745 Answers: 0 Comments: 2

1−1+1−1+1−1+1−1+.....=(1/2) {But it diverges 1+1+1+1+1+1+1+......=−(1/2) {But it diverges 1+2+4+8+16+.....=−1 {But it diverges 1+2+3+4+5+6+7=−(1/(12)) {But it diverges 1−2+4−8+.....=(1/3) {But it diverges 1−2+3−4+5−6+.....=(1/4) {Is it a divergent?????

$$\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+.....=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+......=−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{16}+.....=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}=−\frac{\mathrm{1}}{\mathrm{12}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+.....=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+\mathrm{5}−\mathrm{6}+.....=\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:\:\left\{{Is}\:{it}\:{a}\:{divergent}?????\right. \\ $$

Question Number 102721 Answers: 1 Comments: 1

f(((100x−1)/(50x+1))) = 2x−1 & f^(−1) (3)= p p=?

$$\mathrm{f}\left(\frac{\mathrm{100x}−\mathrm{1}}{\mathrm{50x}+\mathrm{1}}\right)\:=\:\mathrm{2x}−\mathrm{1}\:\&\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{3}\right)=\:\mathrm{p} \\ $$$$\mathrm{p}=? \\ $$

Question Number 102716 Answers: 3 Comments: 0

y′′+3y′−10y=14e^(−5x)

$$\mathrm{y}''+\mathrm{3y}'−\mathrm{10y}=\mathrm{14e}^{−\mathrm{5x}} \\ $$

Question Number 102714 Answers: 0 Comments: 1

Question Number 102705 Answers: 0 Comments: 0

For what values of k (cosA−(1/5))(cosB−(1/5))(cosC−(1/5))≤k hold in all triangles ABC?

$${For}\:{what}\:{values}\:{of}\:{k}\:\left({cosA}−\frac{\mathrm{1}}{\mathrm{5}}\right)\left({cosB}−\frac{\mathrm{1}}{\mathrm{5}}\right)\left({cosC}−\frac{\mathrm{1}}{\mathrm{5}}\right)\leqslant{k} \\ $$$${hold}\:{in}\:{all}\:{triangles}\:{ABC}? \\ $$

Question Number 102701 Answers: 2 Comments: 1

Evaluate: ∫((sin x)/x)dx

$${Evaluate}: \\ $$$$\int\frac{\mathrm{sin}\:{x}}{{x}}{dx} \\ $$

Question Number 102698 Answers: 2 Comments: 0

Question Number 102690 Answers: 3 Comments: 0

(1)∫(1/(cos (√x))) dx (2) ∫ (1/(2+cot x)) dx (3) ∫ (1/(ln(cos x))) dx

$$\left(\mathrm{1}\right)\int\frac{\mathrm{1}}{\mathrm{cos}\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{2}+\mathrm{cot}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{cos}\:\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$

Question Number 102686 Answers: 0 Comments: 1

Σ_(r=1) ^∞ i^r +Σ_(r=0) ^∞ i^r

$$\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{{r}} +\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}{i}^{{r}} \\ $$

Question Number 102664 Answers: 2 Comments: 0

2x=5 x=? −−− for test app only

$$\mathrm{2}{x}=\mathrm{5} \\ $$$${x}=? \\ $$$$−−− \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{test}}\:\boldsymbol{{app}}\:\boldsymbol{{only}} \\ $$

Question Number 102653 Answers: 3 Comments: 0

Question Number 102652 Answers: 0 Comments: 2

2+18+156+1388+...n terms

$$\mathrm{2}+\mathrm{18}+\mathrm{156}+\mathrm{1388}+...{n}\:{terms} \\ $$

Question Number 102651 Answers: 0 Comments: 1

12+14+24+58+164....upto nth terms

$$\mathrm{12}+\mathrm{14}+\mathrm{24}+\mathrm{58}+\mathrm{164}....\mathrm{upto}\:\mathrm{nth}\:\mathrm{terms} \\ $$

Question Number 102644 Answers: 2 Comments: 0

Question Number 102642 Answers: 2 Comments: 0

Question Number 102639 Answers: 1 Comments: 0

(dy/dx) −2xy = 6y e^y^2

$$\frac{{dy}}{{dx}}\:−\mathrm{2}{xy}\:=\:\mathrm{6}{y}\:{e}^{{y}^{\mathrm{2}} } \\ $$

Question Number 102638 Answers: 1 Comments: 6

to Mr W i forgot the formula to find the area of a triangle by using the three height line

$${to}\:{Mr}\:{W} \\ $$$${i}\:{forgot}\:{the}\:{formula}\:{to}\:{find} \\ $$$${the}\:{area}\:{of}\:{a}\:{triangle}\:{by} \\ $$$${using}\:{the}\:{three}\:{height}\:{line} \\ $$

Question Number 102635 Answers: 2 Comments: 0

Question Number 102627 Answers: 3 Comments: 0

show that: cosθ + cos2θ + ....cos nθ= ((cos (1/2)(n +1)θ sin(1/2)nθ)/(sin (1/2)nθ)) Show that: sin θ + sin 2θ + ....+ sin nθ = ((sin (1/2)(n + 1)θ sin(1/2)nθ)/(sin (1/2)nθ)) where θ ∈ R and θ ≠2πk , k ∈Z

$$\mathrm{show}\:\mathrm{that}:\:\mathrm{cos}\theta\:+\:\mathrm{cos2}\theta\:+\:....\mathrm{cos}\:{n}\theta=\:\frac{\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{Show}\:\mathrm{that}:\:\mathrm{sin}\:\theta\:+\:\mathrm{sin}\:\mathrm{2}\theta\:+\:....+\:\mathrm{sin}\:{n}\theta\:=\:\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\:\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{where}\:\theta\:\in\:\mathbb{R}\:\mathrm{and}\:\theta\:\neq\mathrm{2}\pi{k}\:,\:{k}\:\in\mathbb{Z} \\ $$$$ \\ $$

Question Number 102624 Answers: 1 Comments: 4

v2.095 has been uploaded. Changes: Go To: opens in a pop window Drawing: Fix for drawing tool not usable in some countries. Uploaded to playstore.

$$\mathrm{v2}.\mathrm{095}\:\mathrm{has}\:\mathrm{been}\:\mathrm{uploaded}. \\ $$$$\boldsymbol{\mathrm{Changes}}: \\ $$$$\mathrm{Go}\:\mathrm{To}:\:\mathrm{opens}\:\mathrm{in}\:\mathrm{a}\:\mathrm{pop}\:\mathrm{window} \\ $$$$\mathrm{Drawing}:\:\mathrm{Fix}\:\mathrm{for}\:\mathrm{drawing}\:\mathrm{tool}\:\mathrm{not}\:\mathrm{usable} \\ $$$$\mathrm{in}\:\mathrm{some}\:\mathrm{countries}.\: \\ $$$$\mathrm{Uploaded}\:\mathrm{to}\:\mathrm{playstore}. \\ $$

Question Number 102606 Answers: 2 Comments: 1

what is the volume of region bounded by y =x^2 −2x and y=x that is rotated about y=4 ?

$${what}\:{is}\:{the}\:{volume}\:{of}\:{region} \\ $$$${bounded}\:{by}\:{y}\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:{and} \\ $$$${y}={x}\:{that}\:{is}\:{rotated}\:{about} \\ $$$${y}=\mathrm{4}\:? \\ $$

Question Number 102600 Answers: 0 Comments: 0

Question Number 102598 Answers: 2 Comments: 0

Question Number 102588 Answers: 4 Comments: 3

solve 109x +103y = 5 for x,y are integer

$${solve}\:\mathrm{109}{x}\:+\mathrm{103}{y}\:=\:\mathrm{5}\:{for}\:{x},{y}\:{are}\:{integer} \\ $$

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