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Question Number 44096 Answers: 2 Comments: 0

Question Number 44095 Answers: 1 Comments: 0

Question Number 44094 Answers: 2 Comments: 2

Question Number 44092 Answers: 0 Comments: 1

Question Number 44091 Answers: 1 Comments: 0

Question Number 44089 Answers: 0 Comments: 0

Question Number 44088 Answers: 1 Comments: 0

Question Number 44085 Answers: 0 Comments: 6

lim x→0 [((sin ∣x∣)/x)]

$${lim}\:\mathrm{x}\rightarrow\mathrm{0}\:\left[\frac{\mathrm{sin}\:\mid{x}\mid}{{x}}\right] \\ $$

Question Number 44069 Answers: 1 Comments: 1

∫(dx/((x+1)(√(x^2 +2)))) = ?

$$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:=\:? \\ $$

Question Number 44068 Answers: 2 Comments: 0

Question Number 44064 Answers: 0 Comments: 0

Question Number 44063 Answers: 0 Comments: 0

Question Number 44062 Answers: 1 Comments: 0

Question Number 44059 Answers: 1 Comments: 0

Prove that any integer can be expressed as in the form of 4k or4k+_− 1 or 4k+_− 2.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{integer}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\: \\ $$$$\mathrm{as}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{4k}\:\mathrm{or4k}\underset{−} {+}\mathrm{1}\:\mathrm{or}\:\mathrm{4k}\underset{−} {+}\mathrm{2}. \\ $$

Question Number 44051 Answers: 1 Comments: 1

Question Number 44038 Answers: 2 Comments: 0

How many times does the digit 6 appear when writing from 6 to 400 ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{does}\:\mathrm{the}\:\mathrm{digit}\:\mathrm{6}\:\mathrm{appear}\:\mathrm{when}\:\mathrm{writing}\:\mathrm{from}\:\:\mathrm{6}\:\mathrm{to}\:\mathrm{400}\:? \\ $$

Question Number 44035 Answers: 0 Comments: 3

Question Number 44034 Answers: 0 Comments: 1

Let I_1 = ∫_( 1) ^2 (1/(√(1+x^2 ))) dx and I_2 = ∫_( 1) ^2 (1/x) dx. Then

$$\mathrm{Let}\:\:{I}_{\mathrm{1}} =\:\underset{\:\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx}\:\mathrm{and}\:{I}_{\mathrm{2}} =\:\underset{\:\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{{x}}\:{dx}. \\ $$$$\mathrm{Then} \\ $$

Question Number 44172 Answers: 1 Comments: 1

The number of solutions of the equation cos^(−1) ((x^2 −1)/(x^2 +1)) + sin^(−1) ((2x)/(x^2 +1)) +tan^(−1) ((2x)/(x^2 −1))=((2π)/3).

$${The}\:{number}\:{of}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{cos}^{−\mathrm{1}} \frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\:+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{2}\pi}{\mathrm{3}}. \\ $$

Question Number 44029 Answers: 0 Comments: 0

Question Number 44028 Answers: 3 Comments: 1

Show that cos^2 x = (1/2)(1+cos2x)

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{cos2x}\right) \\ $$

Question Number 44026 Answers: 0 Comments: 1

ifA:B=3:6 and B:C = 7:8 find A:B:C solution since B is common then A:B =3:6}7 B:C=7:8}6 A:B=21:42 B:C=42:48 ∴ A :B:C =21:42:48 by Snill James

$${ifA}:{B}=\mathrm{3}:\mathrm{6}\:{and}\:{B}:{C}\:=\:\mathrm{7}:\mathrm{8} \\ $$$${find}\:{A}:{B}:{C} \\ $$$${solution} \\ $$$${since}\:{B}\:{is}\:{common}\:{then} \\ $$$$\left.{A}:{B}\:=\mathrm{3}:\mathrm{6}\right\}\mathrm{7} \\ $$$$\left.{B}:{C}=\mathrm{7}:\mathrm{8}\right\}\mathrm{6} \\ $$$${A}:{B}=\mathrm{21}:\mathrm{42} \\ $$$${B}:{C}=\mathrm{42}:\mathrm{48} \\ $$$$\:\:\:\:\:\:\:\:\therefore\:\:\:{A}\::{B}:{C}\:=\mathrm{21}:\mathrm{42}:\mathrm{48} \\ $$$${by}\:{Snill}\:{James} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 44020 Answers: 1 Comments: 0

Question Number 44017 Answers: 1 Comments: 3

Question Number 44005 Answers: 0 Comments: 0

Question Number 44002 Answers: 0 Comments: 1

calculate I = ∫_0 ^(π/4) ((arctanx)/(1+x)) and J = ∫_0 ^(π/4) ((arctanx)/(1−x))dx

$${calculate}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{arctanx}}{\mathrm{1}+{x}}\:\:\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{arctanx}}{\mathrm{1}−{x}}{dx} \\ $$

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