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Question Number 10095    Answers: 1   Comments: 0

Prove that f(x) = x^2 is continous at x = 2 while f(x) = {_(0 x = 2) ^(x^2 x ≠ 2) is not continous at x = 2

$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:\:\mathrm{is}\:\mathrm{continous}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{while}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left\{_{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{x}\:=\:\mathrm{2}} ^{\mathrm{x}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{x}\:\neq\:\mathrm{2}} \:\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{continous}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2}\right. \\ $$

Question Number 10094    Answers: 1   Comments: 0

Prove that if lim_(x→a) f_1 (x) = L_1 and lim_(x→a) f_2 (x) = L_2 then lim_(x→a) [f_1 (x)+f_2 (x)] = L_1 +L_2

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\:\:\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\:\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{L}_{\mathrm{1}} \:\:\mathrm{and}\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\:\:\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)\:=\:\mathrm{L}_{\mathrm{2}} \:\mathrm{then}\:\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\left[\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)+\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)\right]\:=\:\mathrm{L}_{\mathrm{1}} +\mathrm{L}_{\mathrm{2}} \\ $$

Question Number 10091    Answers: 1   Comments: 0

((a−1)/(b−2)) =(2/3) ,((c+1)/(c−1))=(3/4) ⇒2a−c+10=?

$$\frac{\mathrm{a}−\mathrm{1}}{\mathrm{b}−\mathrm{2}}\:=\frac{\mathrm{2}}{\mathrm{3}}\:\:,\frac{\mathrm{c}+\mathrm{1}}{\mathrm{c}−\mathrm{1}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{2a}−\mathrm{c}+\mathrm{10}=? \\ $$

Question Number 10082    Answers: 0   Comments: 1

(x/6)=(y/4)=(z/k)=k x+y+z=−25 k=?

$$\frac{\mathrm{x}}{\mathrm{6}}=\frac{\mathrm{y}}{\mathrm{4}}=\frac{\mathrm{z}}{\mathrm{k}}=\mathrm{k} \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=−\mathrm{25} \\ $$$$\mathrm{k}=? \\ $$

Question Number 10078    Answers: 0   Comments: 1

Question Number 10076    Answers: 2   Comments: 0

3a=4b=5c 2a+3b−c=146 ⇒c=?

$$\mathrm{3a}=\mathrm{4b}=\mathrm{5c} \\ $$$$\mathrm{2a}+\mathrm{3b}−\mathrm{c}=\mathrm{146} \\ $$$$\Rightarrow\mathrm{c}=? \\ $$

Question Number 10070    Answers: 1   Comments: 0

Find the sum of the digits of , 3333333334^2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:, \\ $$$$\mathrm{3333333334}^{\mathrm{2}} \\ $$

Question Number 10069    Answers: 1   Comments: 2

A man can row a boat at 4 km/hr in still water. He row the boat 2km upstream and 2km back to his starting place in 2 hours. How fast is the stream flowing.

$$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{at}\:\mathrm{4}\:\mathrm{km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}. \\ $$$$\mathrm{He}\:\mathrm{row}\:\mathrm{the}\:\mathrm{boat}\:\mathrm{2km}\:\mathrm{upstream}\:\mathrm{and}\:\mathrm{2km}\:\mathrm{back} \\ $$$$\mathrm{to}\:\mathrm{his}\:\mathrm{starting}\:\mathrm{place}\:\mathrm{in}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{fast}\:\mathrm{is}\: \\ $$$$\mathrm{the}\:\mathrm{stream}\:\mathrm{flowing}. \\ $$

Question Number 10067    Answers: 1   Comments: 0

((a×b×c)/(a+b))=−(1/2) ((a×b×c)/(b+c))=(1/2) ((a×b×c)/(a+c))=1 ⇒a×b×c=?

$$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{a}+\mathrm{b}}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{b}+\mathrm{c}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{a}×\mathrm{b}×\mathrm{c}}{\mathrm{a}+\mathrm{c}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{a}×\mathrm{b}×\mathrm{c}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 10064    Answers: 1   Comments: 0

if a^2 +b^2 =3ab then prove that log((a+b)/(√5))=(1/2)(loga+logb)

$$\mathrm{if}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{3ab}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{log}\frac{\mathrm{a}+\mathrm{b}}{\sqrt{\mathrm{5}}}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{log}{a}+\mathrm{log}{b}\right) \\ $$$$ \\ $$

Question Number 10062    Answers: 1   Comments: 1

Question Number 10056    Answers: 1   Comments: 0

Infrared rays of frequency 1.0 × 10^(13) Hz have a wavelength of 3.0 × 10^(−5) m in a vacuum. The wavelenth of X rays of frequency 5.0 × 10^(16) Hz in a vacuum will be ?

$$\mathrm{Infrared}\:\mathrm{rays}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{1}.\mathrm{0}\:×\:\mathrm{10}^{\mathrm{13}} \:\mathrm{Hz} \\ $$$$\mathrm{have}\:\mathrm{a}\:\mathrm{wavelength}\:\mathrm{of}\:\mathrm{3}.\mathrm{0}\:×\:\mathrm{10}^{−\mathrm{5}} \:\mathrm{m}\:\mathrm{in}\:\mathrm{a}\:\mathrm{vacuum}. \\ $$$$\mathrm{The}\:\mathrm{wavelenth}\:\mathrm{of}\:\mathrm{X}\:\mathrm{rays}\:\mathrm{of}\:\mathrm{frequency} \\ $$$$\mathrm{5}.\mathrm{0}\:×\:\mathrm{10}^{\mathrm{16}} \:\mathrm{Hz}\:\mathrm{in}\:\mathrm{a}\:\mathrm{vacuum}\:\mathrm{will}\:\mathrm{be}\:? \\ $$

Question Number 10050    Answers: 0   Comments: 4

h ow do we know 2017 and another number is a prime number?

$$\mathrm{h}\:\mathrm{ow}\:\mathrm{do}\:\mathrm{we}\:\mathrm{know}\:\mathrm{2017}\:\mathrm{and}\:\mathrm{another}\:\mathrm{number}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}? \\ $$

Question Number 10049    Answers: 0   Comments: 0

3x+4x×5y

$$\mathrm{3x}+\mathrm{4x}×\mathrm{5y} \\ $$

Question Number 10045    Answers: 1   Comments: 0

y⟩0 ((3x^2 −3xy+y^2 )/y^2 )=7 ⇒max(x)=?

$$\mathrm{y}\rangle\mathrm{0} \\ $$$$\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} }=\mathrm{7}\:\Rightarrow\mathrm{max}\left(\mathrm{x}\right)=? \\ $$

Question Number 10043    Answers: 1   Comments: 0

∣x−3∣^(x^2 −9) =1 ⇒Σx=?

$$\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}^{\mathrm{2}} −\mathrm{9}} =\mathrm{1}\:\:\Rightarrow\Sigma\mathrm{x}=? \\ $$

Question Number 10041    Answers: 1   Comments: 0

Question Number 10040    Answers: 1   Comments: 0

Show that ⌊log_(10) (x)+1⌋ give the number of digits for x∈Z

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\lfloor\mathrm{log}_{\mathrm{10}} \left({x}\right)+\mathrm{1}\rfloor\:\:\:\mathrm{give}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{digits}\:\mathrm{for}\:{x}\in\mathbb{Z} \\ $$

Question Number 10039    Answers: 0   Comments: 2

let f(x) and g(x) be twice differentiable functions on [0,2] satisfying f′′(x)=g′′(x), f′(1)=4, g′(1)=6, f(2)=3 and g(2)=9. Then what is f(x)−g(x) at x=4 equal to?

$$ \\ $$$${let}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{be}\:{twice}\:{differentiable} \\ $$$${functions}\:{on}\:\left[\mathrm{0},\mathrm{2}\right]\:{satisfying} \\ $$$${f}''\left({x}\right)={g}''\left({x}\right),\:{f}'\left(\mathrm{1}\right)=\mathrm{4},\:{g}'\left(\mathrm{1}\right)=\mathrm{6}, \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{3}\:{and}\:{g}\left(\mathrm{2}\right)=\mathrm{9}.\:{Then}\:{what}\:{is} \\ $$$${f}\left({x}\right)−{g}\left({x}\right)\:{at}\:{x}=\mathrm{4}\:{equal}\:{to}? \\ $$

Question Number 10035    Answers: 0   Comments: 0

is cos(7x+i5y) analytic function or not

$$\mathrm{is}\:\mathrm{cos}\left(\mathrm{7x}+\mathrm{i5y}\right)\:\mathrm{analytic}\:\mathrm{function}\:\mathrm{or}\:\mathrm{not} \\ $$

Question Number 10034    Answers: 0   Comments: 0

cos(z) is analytic or not explain me

$${cos}\left({z}\right)\:{is}\:{analytic}\:{or}\:{not}\:{explain}\:{me} \\ $$

Question Number 10033    Answers: 1   Comments: 0

Question Number 10031    Answers: 0   Comments: 1

Question Number 10029    Answers: 0   Comments: 1

The first 3 runners in 100m race were clocked 9.5s, 10s, 10.5s respectively. How far is the first from the third runners when the first runner reached the finished line.

$$\mathrm{The}\:\mathrm{first}\:\mathrm{3}\:\mathrm{runners}\:\mathrm{in}\:\mathrm{100m}\:\mathrm{race}\:\mathrm{were}\:\mathrm{clocked} \\ $$$$\mathrm{9}.\mathrm{5s},\:\mathrm{10s},\:\mathrm{10}.\mathrm{5s}\:\mathrm{respectively}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{first}\:\mathrm{from}\:\mathrm{the}\:\mathrm{third}\:\mathrm{runners}\:\mathrm{when}\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{runner}\:\mathrm{reached}\:\mathrm{the}\:\mathrm{finished}\:\mathrm{line}. \\ $$

Question Number 10023    Answers: 2   Comments: 0

Question Number 10022    Answers: 0   Comments: 0

A rectangular building was constructed and its height was twice it frontage. The building was divided into parts by a partition that is 30 feet from the parallel to the front wall. If the near partition of the bulding is 3500 feet. Find the dimension of the building.

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{building}\:\mathrm{was}\:\mathrm{constructed}\:\mathrm{and} \\ $$$$\mathrm{its}\:\mathrm{height}\:\mathrm{was}\:\mathrm{twice}\:\mathrm{it}\:\mathrm{frontage}.\:\mathrm{The}\:\mathrm{building} \\ $$$$\mathrm{was}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{parts}\:\mathrm{by}\:\mathrm{a}\:\mathrm{partition}\:\mathrm{that}\:\mathrm{is} \\ $$$$\mathrm{30}\:\mathrm{feet}\:\mathrm{from}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{front}\:\mathrm{wall}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{near}\:\mathrm{partition}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bulding}\:\mathrm{is}\:\mathrm{3500}\:\mathrm{feet}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\mathrm{the}\:\mathrm{building}. \\ $$

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