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Question Number 73525    Answers: 1   Comments: 2

Question Number 73466    Answers: 1   Comments: 0

please explain this Lim_(x→0) ((sinx)/x) = 1 by l′hopitals theorem Lim_(x→0) ((sinx)/x) = 0 by Squeez theorem is there something wrong?

$${please}\:{explain}\:{this}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\frac{{sinx}}{{x}}\:=\:\mathrm{1}\:\:{by}\:{l}'{hopitals}\:{theorem} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\:\frac{{sinx}}{{x}}\:=\:\mathrm{0}\:{by}\:{Squeez}\:{theorem} \\ $$$${is}\:{there}\:{something}\:{wrong}? \\ $$

Question Number 73405    Answers: 0   Comments: 0

can someone please prove the Chinese Remainder theorem, for modula arithmetic?

$${can}\:{someone}\:{please}\:{prove}\:{the}\: \\ $$$${Chinese}\:{Remainder}\:{theorem},\:{for}\: \\ $$$${modula}\:{arithmetic}? \\ $$

Question Number 73358    Answers: 0   Comments: 1

1/4x2−1/2x−13=0

$$\mathrm{1}/\mathrm{4}{x}\mathrm{2}−\mathrm{1}/\mathrm{2}{x}−\mathrm{13}=\mathrm{0} \\ $$

Question Number 73330    Answers: 1   Comments: 1

find lim_(x→0) ((ln(2−cos(2x)))/(ln(1+xsin(3x))))

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left(\mathrm{2}−{cos}\left(\mathrm{2}{x}\right)\right)}{{ln}\left(\mathrm{1}+{xsin}\left(\mathrm{3}{x}\right)\right)} \\ $$

Question Number 73255    Answers: 1   Comments: 0

Question Number 73235    Answers: 0   Comments: 0

Question Number 73211    Answers: 0   Comments: 0

y=(c+3)(√x) +((3+d)/x)−((a+4)/x^(a+3) )

$${y}=\left({c}+\mathrm{3}\right)\sqrt{{x}}\:+\frac{\mathrm{3}+{d}}{{x}}−\frac{{a}+\mathrm{4}}{{x}^{{a}+\mathrm{3}} } \\ $$

Question Number 73030    Answers: 2   Comments: 0

Question Number 73017    Answers: 0   Comments: 1

find lim_(x→+∞) x(√(x^2 + 1))

$${find}\: \\ $$$$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\:{x}\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\: \\ $$

Question Number 72871    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 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 72806    Answers: 1   Comments: 2

show that lim_( x→0) [ x] does not exist. Hence define [x] and sketch a graph for y = 3x^2 + [x]

$$\underset{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\rightarrow\mathrm{0}} {\:{show}\:{that}\:\:\mathrm{lim}}\:\left[\:{x}\right]\:\:{does}\:{not}\:{exist}. \\ $$$${Hence}\:{define}\:\:\left[{x}\right]\:\:{and}\:{sketch}\:{a}\:{graph}\:{for}\: \\ $$$$\:{y}\:=\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\left[{x}\right] \\ $$

Question Number 72805    Answers: 0   Comments: 0

PARTIAL VARIATION The success rate of government variws inversly as the number of corrupt mi nded individual and varies directly as the number of clean minded individal .if the goverment attain 95% success rate when there are two corrupt minded and 75% success rate when there are 5 corrupt minded and 20 clean minded individual. How many corrupr minded individual must be in administration with one clean minded individual to attain 99% success rate?

$${PARTIAL}\:{VARIATION} \\ $$$${The}\:{success}\:{rate}\:{of}\:{government}\:{variws}\: \\ $$$${inversly}\:{as}\:{the}\:{number}\:{of}\:{corrupt}\:{mi} \\ $$$${nded}\:{individual}\:{and}\:{varies}\:{directly} \\ $$$${as}\:{the}\:{number}\:{of}\:{clean}\:{minded}\:{individal} \\ $$$$.{if}\:\:{the}\:{goverment}\:{attain}\:\mathrm{95\%}\:{success} \\ $$$${rate}\:{when}\:{there}\:{are}\:{two}\:{corrupt}\:{minded} \\ $$$${and}\:\mathrm{75\%}\:{success}\:{rate}\:{when}\:{there}\:{are} \\ $$$$\mathrm{5}\:{corrupt}\:{minded}\:{and}\:\mathrm{20}\:{clean}\:{minded} \\ $$$${individual}.\:{How}\:{many}\:{corrupr}\:{minded} \\ $$$${individual}\:{must}\:{be}\:{in}\:{administration}\: \\ $$$${with}\:{one}\:{clean}\:{minded}\:{individual}\:{to}\: \\ $$$${attain}\:\mathrm{99\%}\:{success}\:{rate}? \\ $$

Question Number 72734    Answers: 3   Comments: 0

A triangle ABC is inscribed in a circle.AC=10cm,BC=7cm and AB=10cm.Find the radius of the circle.

$${A}\:{triangle}\:{ABC}\:{is}\:{inscribed}\:{in}\:{a} \\ $$$${circle}.{AC}=\mathrm{10}{cm},{BC}=\mathrm{7}{cm}\:{and}\: \\ $$$${AB}=\mathrm{10}{cm}.{Find}\:{the}\:{radius}\:{of}\:{the} \\ $$$${circle}. \\ $$

Question Number 72718    Answers: 0   Comments: 3

given that a ≡ b(mod n) show that a^k ≡ b^k (mod n)

$${given}\:{that}\: \\ $$$$\:{a}\:\equiv\:{b}\left({mod}\:{n}\right)\: \\ $$$${show}\:{that}\:{a}^{{k}} \:\equiv\:{b}^{{k}} \:\left({mod}\:{n}\right) \\ $$

Question Number 72688    Answers: 3   Comments: 0

Evaluate lim_(t→9) ((9−t)/(3−(√t) ))

$${Evaluate}\: \\ $$$$\:\underset{{t}\rightarrow\mathrm{9}} {\:{lim}}\frac{\mathrm{9}−{t}}{\mathrm{3}−\sqrt{{t}}\:} \\ $$

Question Number 72693    Answers: 1   Comments: 0

prove that the arithmetic mean of a sequence is greater or equal to the geometric mean. that is ((a + b)/2) ≥ (√(ab))

$${prove}\:{that}\:{the}\:{arithmetic}\:{mean}\:{of}\:{a}\:{sequence} \\ $$$${is}\:{greater}\:{or}\:{equal}\:{to}\:{the}\:{geometric}\:{mean}. \\ $$$${that}\:\:{is}\:\: \\ $$$$\:\:\:\:\frac{{a}\:+\:{b}}{\mathrm{2}}\:\geqslant\:\sqrt{{ab}}\: \\ $$

Question Number 72634    Answers: 1   Comments: 4

help me with the conditions please for a function f to be continuous at a point a

$${help}\:{me}\:{with}\:{the}\:{conditions}\:{please}\: \\ $$$${for}\:{a}\:{function}\:{f}\:{to}\:{be}\:{continuous}\:{at}\:{a}\:{point}\:{a} \\ $$

Question Number 72633    Answers: 0   Comments: 0

prove using th sandwich or Squeez theorem that for any a > 0 lim_(x→a) (√x) = (√a)

$${prove}\:{using}\:{th}\:{sandwich}\:{or}\:{Squeez}\:{theorem}\:{that} \\ $$$${for}\:{any}\:\:{a}\:>\:\mathrm{0} \\ $$$$\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$

Question Number 72628    Answers: 0   Comments: 2

solve the inequality log_3 (2x^2 + 9x + 9) < 0

$${solve}\:{the}\:{inequality}\: \\ $$$$\:\:{log}_{\mathrm{3}} \left(\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:+\:\mathrm{9}\right)\:<\:\mathrm{0} \\ $$

Question Number 72595    Answers: 1   Comments: 3

(α+β)^2 = α^2 + 2αβ + β^(2 )

$$\left(\alpha+\beta\right)^{\mathrm{2}} \:=\:\alpha^{\mathrm{2}} \:+\:\mathrm{2}\alpha\beta\:+\:\beta^{\mathrm{2}\:} \\ $$

Question Number 72579    Answers: 1   Comments: 0

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