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Question Number 54371 Answers: 1 Comments: 1

prove that ln(z) = ∫_0 ^1 ((z−1)/(1+t(z−1)))dt .

$${prove}\:{that}\:{ln}\left({z}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{z}−\mathrm{1}}{\mathrm{1}+{t}\left({z}−\mathrm{1}\right)}{dt}\:. \\ $$

Question Number 54369 Answers: 0 Comments: 2

find lim_(x→1) (ξ(x)−(1/(x−1)))

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\left(\xi\left({x}\right)−\frac{\mathrm{1}}{{x}−\mathrm{1}}\right) \\ $$

Question Number 54367 Answers: 1 Comments: 1

find ∫_1 ^(+∞) (([t])/t) t^(−p) dt interms of ξ(p) with p>0 .

$${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[{t}\right]}{{t}}\:{t}^{−{p}} {dt}\:{interms}\:{of}\:\xi\left({p}\right)\:{with}\:{p}>\mathrm{0}\:. \\ $$

Question Number 54364 Answers: 1 Comments: 0

If p is the measure of per pendicular segment from the origin on the line whose intercept are a and b.show that (1/a^2 )+(1/b^2 )=(1/p^2 )

$$\mathrm{If}\:\:\mathrm{p}\:\mathrm{is}\:\mathrm{the}\:\mathrm{measure}\:\mathrm{of}\:\mathrm{per} \\ $$$$\mathrm{pendicular}\:\mathrm{segment}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{origin}\:\mathrm{on}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{whose}\:\mathrm{intercept}\:\mathrm{are} \\ $$$$\mathrm{a}\:\:\mathrm{and}\:\:\:\:\mathrm{b}.\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{p}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 54360 Answers: 2 Comments: 1

Question Number 54357 Answers: 2 Comments: 1

Question Number 54353 Answers: 0 Comments: 1

What is ∪,∩?? I want to know plz :) Have a nice day !

$${What}\:{is}\:\cup,\cap?? \\ $$$$\left.{I}\:{want}\:{to}\:{know}\:\mathrm{plz}\::\right) \\ $$$${Have}\:{a}\:{nice}\:{day}\:! \\ $$

Question Number 54341 Answers: 1 Comments: 0

Question Number 58312 Answers: 0 Comments: 4

Show that the angle θ between two unit vectors a_ ^ and b_ ^ is given by cosθ=a_ ^ •b_ ^ . Hence, given that a_ ^ =i_ cosA+j_ sinA and b_ ^ =i_ cosB−j_ sinB, prove that cos(A+B)= cosAcosB−sinAsinB.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angle}\:\theta\:\mathrm{between}\:\mathrm{two}\:\mathrm{unit} \\ $$$$\mathrm{vectors}\:\underset{} {\hat {\mathrm{a}}}\:\mathrm{and}\:\underset{} {\hat {\mathrm{b}}}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{cos}\theta=\underset{} {\hat {\mathrm{a}}}\bullet\underset{} {\hat {\mathrm{b}}}. \\ $$$$\mathrm{Hence},\:\mathrm{given}\:\mathrm{that}\:\underset{} {\hat {\mathrm{a}}}=\underset{} {\mathrm{i}cosA}+\underset{} {\mathrm{j}sinA}\:\mathrm{and} \\ $$$$\underset{} {\hat {\mathrm{b}}}=\underset{} {\mathrm{i}cosB}−\underset{} {\mathrm{j}sinB},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{cos}\left(\mathrm{A}+\mathrm{B}\right)= \\ $$$$\mathrm{cosAcosB}−\mathrm{sinAsinB}. \\ $$

Question Number 58313 Answers: 2 Comments: 2

Question Number 54334 Answers: 1 Comments: 1

Question Number 54322 Answers: 3 Comments: 0

Question Number 54312 Answers: 1 Comments: 2

Question Number 54289 Answers: 2 Comments: 5

Question Number 54286 Answers: 2 Comments: 2

Question Number 54281 Answers: 0 Comments: 1

Question Number 54278 Answers: 0 Comments: 4

If f be n→n (n∈N) and is increasing, f(f(n))=3n; find f(2). options: 1, 2, 3,4 .

$${If}\:{f}\:{be}\:{n}\rightarrow{n}\:\:\:\left({n}\in\mathbb{N}\right)\:{and}\:{is}\:{increasing}, \\ $$$${f}\left({f}\left({n}\right)\right)=\mathrm{3}{n};\:{find}\:{f}\left(\mathrm{2}\right). \\ $$$${options}:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\mathrm{4}\:. \\ $$

Question Number 54271 Answers: 1 Comments: 1

Question Number 54270 Answers: 2 Comments: 0

Find the equation to two circles which touch the x−axis at the origin and also touch the line 12x+5y=60

$${Find}\:{the}\:{equation}\:{to}\:{two} \\ $$$${circles}\:{which}\:{touch}\:{the}\: \\ $$$${x}−{axis}\:{at}\:{the}\:{origin} \\ $$$${and}\:{also}\:{touch}\:{the}\:{line} \\ $$$$\mathrm{12}{x}+\mathrm{5}{y}=\mathrm{60} \\ $$

Question Number 54268 Answers: 0 Comments: 1

Question Number 54259 Answers: 1 Comments: 1

Question Number 54258 Answers: 0 Comments: 1

Question Number 54273 Answers: 2 Comments: 0

Question Number 54248 Answers: 2 Comments: 1

Question Number 54242 Answers: 2 Comments: 0

Question Number 54240 Answers: 1 Comments: 1

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