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Question Number 180495 Answers: 1 Comments: 0

Question Number 180490 Answers: 3 Comments: 0

Question Number 180485 Answers: 0 Comments: 1

Determine the value of a and b , that make the function f(x) continuity f(x) = { ((x + 3 ,x ≨ 4)),((2ax + b ,x = 4)),((x^2 −3 , x ≩ 4)) :}

$${Determine}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:, \\ $$$$\:{that}\:{make}\:{the}\:{function}\:{f}\left({x}\right)\:{continuity} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{{x}\:+\:\mathrm{3}\:\:\:\:\:,{x}\:\lneqq\:\mathrm{4}}\\{\mathrm{2}{ax}\:+\:{b}\:\:\:\:,{x}\:=\:\mathrm{4}}\\{{x}^{\mathrm{2}} −\mathrm{3}\:\:\:,\:{x}\:\gneqq\:\mathrm{4}}\end{cases} \\ $$

Question Number 180483 Answers: 0 Comments: 1

Question Number 180471 Answers: 0 Comments: 1

Question Number 180467 Answers: 1 Comments: 0

Question Number 180459 Answers: 2 Comments: 0

Question Number 180458 Answers: 2 Comments: 0

Question Number 180457 Answers: 1 Comments: 11

Question Number 180449 Answers: 0 Comments: 1

x + y + z = 0 2x + 4y − z = 0 3x + 2y + 2z = 0 Solve for x,y,and z

$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{0} \\ $$$$\mathrm{2x}\:+\:\mathrm{4y}\:−\:\mathrm{z}\:=\:\mathrm{0} \\ $$$$\mathrm{3x}\:+\:\mathrm{2y}\:+\:\mathrm{2z}\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\mathrm{y},\mathrm{and}\:\mathrm{z} \\ $$

Question Number 180447 Answers: 0 Comments: 1

x + y − z = 0 2x − 3y + z = 0 x −4y + 2z = 0 find the value of x,y, and z

$$\mathrm{x}\:+\:\mathrm{y}\:−\:\mathrm{z}\:=\:\mathrm{0} \\ $$$$\mathrm{2x}\:−\:\mathrm{3y}\:+\:\mathrm{z}\:=\:\mathrm{0} \\ $$$$\mathrm{x}\:−\mathrm{4y}\:+\:\mathrm{2z}\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\mathrm{y},\:\mathrm{and}\:\mathrm{z} \\ $$

Question Number 180446 Answers: 2 Comments: 0

Solve : x_1 + 2x_2 − 3x_3 = 0 2x_1 + 4x_2 − 2x_3 = 2 3x_1 + 6x_2 − 4x_3 = 3

$$\mathrm{Solve}\::\: \\ $$$$\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{2x}_{\mathrm{2}} \:−\:\mathrm{3x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$\mathrm{2x}_{\mathrm{1}} \:+\:\mathrm{4x}_{\mathrm{2}} \:−\:\mathrm{2x}_{\mathrm{3}} \:=\:\mathrm{2} \\ $$$$\mathrm{3x}_{\mathrm{1}} \:+\:\mathrm{6x}_{\mathrm{2}} \:−\:\mathrm{4x}_{\mathrm{3}} \:=\:\mathrm{3} \\ $$

Question Number 180438 Answers: 3 Comments: 0

lim_(x→0) (((√(4+x))−(√(4−x)))/x) find the limit above

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\sqrt{\mathrm{4}+\mathrm{x}}−\sqrt{\mathrm{4}−\mathrm{x}}}{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{above} \\ $$

Question Number 180436 Answers: 0 Comments: 0

f(x−y)+f(x+y)=2f(x)f(y) find f(x) Q#180407 (Altered)

$${f}\left({x}−{y}\right)+{f}\left({x}+{y}\right)=\mathrm{2}{f}\left({x}\right){f}\left({y}\right) \\ $$$$\mathrm{find}\:{f}\left({x}\right) \\ $$$${Q}#\mathrm{180407}\:\left({Altered}\right) \\ $$

Question Number 180423 Answers: 2 Comments: 4

Question Number 180421 Answers: 2 Comments: 0

find the number of numbers less than 10^6 which contain at least 3 different digits.

$${find}\:{the}\:{number}\:{of}\:{numbers}\:{less}\:{than}\: \\ $$$$\mathrm{10}^{\mathrm{6}} \:{which}\:{contain}\:{at}\:{least}\:\mathrm{3}\:{different} \\ $$$${digits}. \\ $$

Question Number 180414 Answers: 1 Comments: 0

lim_(x→3) (((3^x −x^3 )/(x^x −3^3 ))) find the limit above

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{3}} {\mathrm{m}}\left(\frac{\mathrm{3}^{\mathrm{x}} −\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{x}} −\mathrm{3}^{\mathrm{3}} }\right) \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{above} \\ $$

Question Number 180413 Answers: 2 Comments: 0

lim_(h→0) (((e^h −1)/h)) find the limit above

$$\mathrm{li}\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{m}}\left(\frac{\mathrm{e}^{\mathrm{h}} −\mathrm{1}}{\mathrm{h}}\right) \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{above} \\ $$

Question Number 180407 Answers: 2 Comments: 0

f(x−y)+f(x+y)=f(x)f(y) find f(x)

$${f}\left({x}−{y}\right)+{f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right) \\ $$$$\mathrm{find}\:{f}\left({x}\right) \\ $$

Question Number 180405 Answers: 0 Comments: 0

Ω = ∫ ((ln (x+1))/(x^2 +x)) dx =?

$$\:\:\:\Omega\:=\:\int\:\frac{\mathrm{ln}\:\left(\mathrm{x}+\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 180400 Answers: 2 Comments: 1

Area BEF=AreaCDF Prouve AD×BE=AE×CD

$$\mathrm{Area}\:\mathrm{BEF}=\mathrm{AreaCDF} \\ $$$$\mathrm{Prouve}\:\:\mathrm{AD}×\mathrm{BE}=\mathrm{AE}×\mathrm{CD} \\ $$

Question Number 180398 Answers: 1 Comments: 1

∫(1/(sin (x−a)sin (x−b)))dx=?

$$\int\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{a}\right)\mathrm{sin}\:\left(\mathrm{x}−\mathrm{b}\right)}\mathrm{dx}=? \\ $$$$ \\ $$

Question Number 180396 Answers: 0 Comments: 0

The difference between the ages of Sammy and Cindy is half the difference between the ages of their parents. Their father is 6 years older than twice the age of Cindy. Their mother is twice as old as Cindy and 12 years older than Sammy. By how many years is Sammy younger than Cindy?

$$\mathrm{The}\:\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ages}\:\mathrm{of} \\ $$$$\mathrm{Sammy}\:\mathrm{and}\:\mathrm{Cindy}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\: \\ $$$$\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ages}\:\mathrm{of}\: \\ $$$$\mathrm{their}\:\mathrm{parents}.\:\mathrm{Their}\:\mathrm{father}\:\mathrm{is}\:\mathrm{6} \\ $$$$\mathrm{years}\:\mathrm{older}\:\mathrm{than}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{age}\:\mathrm{of}\: \\ $$$$\mathrm{Cindy}.\:\mathrm{Their}\:\mathrm{mother}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{as}\:\mathrm{old} \\ $$$$\mathrm{as}\:\mathrm{Cindy}\:\mathrm{and}\:\mathrm{12}\:\mathrm{years}\:\mathrm{older}\:\mathrm{than}\: \\ $$$$\mathrm{Sammy}.\:\mathrm{By}\:\mathrm{how}\:\mathrm{many}\:\mathrm{years}\:\mathrm{is}\: \\ $$$$\mathrm{Sammy}\:\mathrm{younger}\:\mathrm{than}\:\mathrm{Cindy}? \\ $$

Question Number 180391 Answers: 1 Comments: 1

y = x − (2/x) Find the set of values of the function.

$$\mathrm{y}\:=\:\mathrm{x}\:−\:\frac{\mathrm{2}}{\mathrm{x}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}. \\ $$

Question Number 180388 Answers: 1 Comments: 0

Question Number 180381 Answers: 2 Comments: 0

(√((8^(12) +4^(13) )/(8^6 +4^(14) )))

$$\sqrt{\frac{\mathrm{8}^{\mathrm{12}} +\mathrm{4}^{\mathrm{13}} }{\mathrm{8}^{\mathrm{6}} +\mathrm{4}^{\mathrm{14}} }} \\ $$

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