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Question Number 52206 Answers: 0 Comments: 1

lim_(x→0) (((1+x)^(1/x) −c)/x)=−(c/2)

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

Question Number 52208 Answers: 1 Comments: 3

Question Number 52214 Answers: 2 Comments: 4

Question Number 52200 Answers: 0 Comments: 0

proof that (√z^2 ) ≠ z , z ∈ C example i=(√(−1)) i^2 =−1 i^4 =1 (√(i^4 )) ≠ i^2 (√1) ≠ −1 1 ≠ −1

$$\mathrm{proof}\:\mathrm{that}\: \\ $$$$\sqrt{{z}^{\mathrm{2}} }\:\neq\:{z}\:,\:{z}\:\in\:\mathbb{C} \\ $$$$\mathrm{example} \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$${i}^{\mathrm{4}} =\mathrm{1} \\ $$$$\sqrt{{i}^{\mathrm{4}} \:}\:\neq\:{i}^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{1}}\:\neq\:−\mathrm{1} \\ $$$$\mathrm{1}\:\neq\:−\mathrm{1} \\ $$$$ \\ $$

Question Number 52198 Answers: 2 Comments: 0

Question Number 52197 Answers: 1 Comments: 0

calculate ∫_(π/4) ^(π/3) ((cosx −sinx)/(2 +sin(2x)))dx

$${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{{cosx}\:−{sinx}}{\mathrm{2}\:+{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$$$ \\ $$

Question Number 52182 Answers: 0 Comments: 1

Question Number 52190 Answers: 2 Comments: 3

Question Number 52164 Answers: 2 Comments: 4

find: ∫_0 ^Π (cos^6 θ −cos^4 θ) dθ plase help me in cinding this And also explain if possible

$${find}: \\ $$$$\underset{\mathrm{0}} {\overset{\Pi} {\int}}\left({cos}^{\mathrm{6}} \theta\:−\mathrm{cos}\:^{\mathrm{4}} \theta\right)\:{d}\theta \\ $$$${plase}\:{help}\:{me}\:{in}\:{cinding}\:{this}\:{And}\:{also} \\ $$$${explain}\:{if}\:{possible} \\ $$

Question Number 52161 Answers: 2 Comments: 7

Question Number 52129 Answers: 1 Comments: 5

Question Number 52124 Answers: 1 Comments: 0

The curve y = ax + (b/(2x− 1)) has the stationary point at (2, 7) . Find the value of a and b .

$$\mathrm{The}\:\mathrm{curve}\:\mathrm{y}\:=\:\mathrm{ax}\:+\:\frac{\mathrm{b}}{\mathrm{2x}−\:\mathrm{1}}\:\mathrm{has}\:\mathrm{the}\:\mathrm{stationary}\:\mathrm{point}\:\mathrm{at}\:\:\left(\mathrm{2},\:\mathrm{7}\right)\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:. \\ $$

Question Number 52123 Answers: 1 Comments: 1

Find lim_(x→∞) ((sin x)/x).

$$\mathrm{Find}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}. \\ $$

Question Number 52108 Answers: 1 Comments: 0

Question Number 52103 Answers: 2 Comments: 0

((×−0.1)/(×+0.1))=((1.2)/(1.7)) Sir plz help me

$$\frac{×−\mathrm{0}.\mathrm{1}}{×+\mathrm{0}.\mathrm{1}}=\frac{\mathrm{1}.\mathrm{2}}{\mathrm{1}.\mathrm{7}}\:\:\:\:\:\:\:\:\:\:\mathrm{Sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 52099 Answers: 1 Comments: 1

Question Number 52091 Answers: 2 Comments: 1

3^x +4^x =5^x find x BY ISHOLA

$$\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \\ $$$${find}\:{x} \\ $$$${BY}\:{ISHOLA} \\ $$

Question Number 52089 Answers: 0 Comments: 0

Question Number 52088 Answers: 0 Comments: 0

determine the value of 5e^(0.5 ) correct to 5 significant fig using d power series of e^x

$${determine}\:{the}\:{value}\:{of}\:\mathrm{5}{e}^{\mathrm{0}.\mathrm{5}\:} \:{correct}\:{to}\:\mathrm{5}\:{significant}\:{fig}\:{using}\:{d}\:{power}\:{series}\:{of}\:{e}^{{x}} \\ $$

Question Number 52087 Answers: 1 Comments: 1

If 1,a_1 ,a_2 ,...,a_(n−1) are n^(th) roots of unity the find the value of (1/(1+1))+(1/(1+a_1 ))+(1/(1+a_2 ))+..+(1/(1+a_(n−1) )) n is odd number

$$\mathrm{If}\:\mathrm{1},{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,...,{a}_{{n}−\mathrm{1}} \:\mathrm{are}\:{n}^{{th}} \:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{unity}\:\mathrm{the}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{1}+{a}_{\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{1}+{a}_{\mathrm{2}} }+..+\frac{\mathrm{1}}{\mathrm{1}+{a}_{{n}−\mathrm{1}} } \\ $$$${n}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{number} \\ $$

Question Number 52086 Answers: 1 Comments: 3

If 1,a_(1,) a_2 ,...,a_(n−1) are n^(th) roots of unity, then prove that. (1+a_1 )(1+a_2 )..(1+a_(n−1) )= n if n is even 0 if n is odd

$$\mathrm{If}\:\mathrm{1},{a}_{\mathrm{1},} {a}_{\mathrm{2}} ,...,{a}_{{n}−\mathrm{1}} \:\mathrm{are}\:{n}^{{th}} \:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{unity},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}. \\ $$$$\left(\mathrm{1}+{a}_{\mathrm{1}} \right)\left(\mathrm{1}+{a}_{\mathrm{2}} \right)..\left(\mathrm{1}+{a}_{{n}−\mathrm{1}} \right)= \\ $$$${n}\:\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{even} \\ $$$$\mathrm{0}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$

Question Number 52082 Answers: 1 Comments: 1

Question Number 52079 Answers: 1 Comments: 1

Sum to the n terms of the series whose n^(th ) term is 2^(n−1 ) + 8n^3 −6n^2

$${Sum}\:{to}\:{the}\:{n}\:{terms}\:{of}\:{the}\:{series}\:{whose}\:{n}^{{th}\:} \:{term}\:{is}\:\mathrm{2}^{{n}−\mathrm{1}\:} \:+\:\mathrm{8}{n}^{\mathrm{3}} \:−\mathrm{6}{n}^{\mathrm{2}} \\ $$

Question Number 52075 Answers: 0 Comments: 0

Question Number 52072 Answers: 0 Comments: 0

Question Number 52061 Answers: 2 Comments: 3

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