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let f(x)=∫_(π/6) ^(π/4) ((tant)/(2+x cost))dt with x real 1)determine a explicit form for f(x) 2)determine also g(x)=∫_(π/6) ^(π/4) ((tant)/((2+xcost)^2 ))dx 3) find the value of ∫_(π/6) ^(π/4) ((tant)/((2+3cost)))dt and ∫_(π/6) ^(π/4) ((tant)/((2+3cost)^2 ))dt

Question Number 72886 Answers: 1 Comments: 0

let w=f(x, y) be a differentiable function where x=rcosθ and y=rsinθ show that (f_x )^2 +(f_y )^2 =(w_x )^2 +1/r^2 (w_y )^2 ? help me sir

$${let}\:{w}={f}\left({x},\:{y}\right)\:{be}\:{a}\:{differentiable}\:{function}\:{where}\:{x}={rcos}\theta\:{and}\:{y}={rsin}\theta\:{show}\:{that}\:\left({f}_{{x}} \right)^{\mathrm{2}} +\left({f}_{{y}} \right)^{\mathrm{2}} =\left({w}_{{x}} \right)^{\mathrm{2}} +\mathrm{1}/{r}^{\mathrm{2}} \left({w}_{{y}} \right)^{\mathrm{2}} ? \\ $$$${help}\:{me}\:{sir}\: \\ $$

Question Number 72884 Answers: 0 Comments: 1

find the area of the region bounded by the semicircle y=(√(a^2 −x^2 )) and the x=+−a and the line y=−a ? by using intigiral pleas sir help me

$${find}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bounded}\:{by}\:{the}\:{semicircle}\:{y}=\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{and}\:{the}\:{x}=+−{a}\:\:{and}\:{the}\:{line}\:{y}=−{a}\:?\:{by}\:{using}\:{intigiral} \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 72883 Answers: 1 Comments: 0

if w=f(u and v) where f_(uu) +f_(vv) =0 and u=(x^2 −y^2 )/2 and v=xy show that w_(xx) +w_(yy) =0 ? pleas sir help me

$${if}\:{w}={f}\left({u}\:{and}\:{v}\right)\:{where}\:{f}_{{uu}} +{f}_{{vv}} =\mathrm{0}\:{and}\:{u}=\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)/\mathrm{2}\:{and}\:{v}={xy}\:{show}\:{that}\:{w}_{{xx}} +{w}_{{yy}} =\mathrm{0}\:? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 72889 Answers: 1 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/((2n+1)n^2 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right){n}^{\mathrm{2}} } \\ $$

Question Number 72880 Answers: 0 Comments: 0

Question Number 72877 Answers: 0 Comments: 1

by using theorem demwover find x^4 =1? pleas sir help me

$${by}\:{using}\:{theorem}\:{demwover}\:{find}\:\:{x}^{\mathrm{4}} =\mathrm{1}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 72871 Answers: 1 Comments: 0

Question Number 72863 Answers: 0 Comments: 1

Question Number 72905 Answers: 2 Comments: 3

f(x)≥0, and lim_(x→a) f(x)=0,lim_(x→a) g(x)=∞ then lim_(x→a) f(x)^(g(x)) =?

$${f}\left({x}\right)\geqslant\mathrm{0},\:{and}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{0},\underset{{x}\rightarrow{a}} {\mathrm{lim}}{g}\left({x}\right)=\infty \\ $$$${then}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)^{{g}\left({x}\right)} =? \\ $$

Question Number 72894 Answers: 1 Comments: 0

Question Number 72841 Answers: 1 Comments: 3

Could someone help me on this question? Knowing that the area of a circle segment is given by A=R^2 (θ−sinθ)/2. Where A=7m^2 ; R^2 =((28)/π). What is the best answer for the angle value (degree) a) 85°<θ<90° b) 95°<θ<100° c) 105°<θ<110° d) 115°<θ<120° e) 125°<θ<135°

$${Could}\:{someone}\:{help}\:{me}\:{on}\:{this}\:{question}? \\ $$$${Knowing}\:{that}\:{the}\:{area}\:{of}\:{a}\:{circle}\:{segment}\:{is}\:{given}\:{by}\:{A}={R}^{\mathrm{2}} \left(\theta−{sin}\theta\right)/\mathrm{2}.\:{Where}\:{A}=\mathrm{7}{m}^{\mathrm{2}} ;\:{R}^{\mathrm{2}} =\frac{\mathrm{28}}{\pi}. \\ $$$${What}\:{is}\:{the}\:{best}\:{answer}\:{for}\:{the}\:{angle}\:{value}\:\left({degree}\right) \\ $$$$\left.{a}\right)\:\mathrm{85}°<\theta<\mathrm{90}° \\ $$$$\left.{b}\right)\:\mathrm{95}°<\theta<\mathrm{100}° \\ $$$$\left.{c}\right)\:\mathrm{105}°<\theta<\mathrm{110}° \\ $$$$\left.{d}\right)\:\mathrm{115}°<\theta<\mathrm{120}° \\ $$$$\left.{e}\right)\:\mathrm{125}°<\theta<\mathrm{135}° \\ $$

Question Number 72838 Answers: 0 Comments: 1

given that f(x) = ((∣x −2∣)/(1−∣x∣)) check if f is continuous a x = 2 hence write f(x) as a pairwise function

$${given}\:{that}\:\:\:{f}\left({x}\right)\:=\:\frac{\mid{x}\:−\mathrm{2}\mid}{\mathrm{1}−\mid{x}\mid} \\ $$$${check}\:{if}\:{f}\:{is}\:{continuous}\:{a}\:{x}\:=\:\mathrm{2} \\ $$$${hence}\:\:{write}\:{f}\left({x}\right)\:{as}\:{a}\:{pairwise}\:{function}\: \\ $$

Question Number 72837 Answers: 0 Comments: 1

find lim_(x→0) x + [x]

$${find}\: \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\:+\:\left[{x}\right] \\ $$

Question Number 72836 Answers: 1 Comments: 1

Question Number 72835 Answers: 1 Comments: 0

In an arithmetic progression the ninth term is greater than the second term and the sum of the first term with the fifth term is 20. What is the fifth term?

$${In}\:{an}\:{arithmetic}\:{progression}\:{the} \\ $$$${ninth}\:{term}\:{is}\:{greater}\:{than}\:{the}\:{second} \\ $$$${term}\:{and}\:{the}\:{sum}\:{of}\:{the}\:{first}\:{term} \\ $$$${with}\:{the}\:{fifth}\:{term}\:{is}\:\mathrm{20}.\:{What}\:{is} \\ $$$${the}\:{fifth}\:{term}? \\ $$

Question Number 72832 Answers: 1 Comments: 1

In a parallelogram OABC, OA^⇁ =a^(−⇁) , OC^→ =c^→ , D is a point such that AD^→ :DB^→ =1:2 Express the following in terms of a and c (i)CB^→ (ii)BC^→ (iii)AB^→ (iv) AD^→ (v)OD^→ (vi)DC^→

Question Number 72824 Answers: 1 Comments: 0

fnd all integers n for which 13∣ 4(n^2 + 1)

$${fnd}\:{all}\:{integers}\:{n}\:{for}\:{which}\: \\ $$$$\:\mathrm{13}\mid\:\mathrm{4}\left({n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$

Question Number 72823 Answers: 1 Comments: 0

What is derivative for this function a×b^(x−1) ×c^((1/2)(x−1)(x−2)) ×d^((1/6)(x−1)(x−2)(x−3))

$$\mathrm{What}\:\mathrm{is}\:\mathrm{derivative}\:\mathrm{for}\:\mathrm{this}\:\mathrm{function} \\ $$$$\: \\ $$$${a}×{b}^{{x}−\mathrm{1}} ×{c}^{\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)} ×{d}^{\frac{\mathrm{1}}{\mathrm{6}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)} \\ $$

Question Number 72934 Answers: 1 Comments: 0

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