Question and Answers Forum

AllQuestion and Answers: Page 1326

Question Number 73572 Answers: 0 Comments: 1

determine wether or not the function f,where f(x) = { ((2x + 1, 0≤ x <2)),((7−x, 2 ≤ x < 4)),((((3x)/4) , 4 ≤ x < 6)) :} is continuous in the interval [0,6[

$${determine}\:{wether}\:{or}\:{not}\:{the}\:{function}\:{f},{where} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2}{x}\:+\:\mathrm{1},\:\mathrm{0}\leqslant\:{x}\:<\mathrm{2}}\\{\mathrm{7}−{x},\:\:\:\mathrm{2}\:\leqslant\:{x}\:<\:\mathrm{4}}\\{\frac{\mathrm{3}{x}}{\mathrm{4}}\:,\:\:\mathrm{4}\:\leqslant\:{x}\:<\:\mathrm{6}}\end{cases} \\ $$$${is}\:{continuous}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{6}\left[\right.\right. \\ $$

Question Number 73570 Answers: 0 Comments: 1

f : x → { ((1 + x, if x<1)),((2x−1,if x>1)) :} investigate the existence and non existence of the limit of f at the point x =1

$${f}\::\:{x}\:\rightarrow\:\begin{cases}{\mathrm{1}\:+\:{x},\:{if}\:{x}<\mathrm{1}}\\{\mathrm{2}{x}−\mathrm{1},{if}\:{x}>\mathrm{1}}\end{cases} \\ $$$${investigate}\:{the}\:{existence}\:{and}\:{non}\:{existence}\:{of}\:{the} \\ $$$${limit}\:{of}\:{f}\:{at}\:{the}\:{point}\:{x}\:=\mathrm{1} \\ $$

Question Number 73569 Answers: 0 Comments: 2

let f(x) = ((tanx)/(tan2x)) . Find the points of discontinuity of f on [0,2π] and determine wether each duscontinuity is a point discontinuity,a jump discontinuity,or a vertical asymtote

$${let}\:{f}\left({x}\right)\:=\:\frac{{tanx}}{{tan}\mathrm{2}{x}}\:.\:{Find}\:{the}\:{points}\:{of}\:{discontinuity} \\ $$$${of}\:{f}\:{on}\:\left[\mathrm{0},\mathrm{2}\pi\right]\:{and}\:{determine}\:{wether}\:{each}\:{duscontinuity}\:{is} \\ $$$${a}\:{point}\:{discontinuity},{a}\:{jump}\:{discontinuity},{or}\:{a}\:{vertical}\:{asymtote} \\ $$$$ \\ $$

Question Number 73567 Answers: 0 Comments: 2

Determine the value of a and b fir which the function f,defined by f(x) = { ((−2sinx, x < −(π/2))),((asinx + b,−(π/2) ≤ x < (π/2))),((cosx, x > (π/2))) :} is continouos

$${Determine}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:{fir}\:{which}\:{the}\:{function}\:{f},{defined}\:{by} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{−\mathrm{2}{sinx},\:\:{x}\:<\:−\frac{\pi}{\mathrm{2}}}\\{{asinx}\:+\:{b},−\frac{\pi}{\mathrm{2}}\:\leqslant\:{x}\:<\:\frac{\pi}{\mathrm{2}}}\\{{cosx},\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:>\:\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$${is}\:{continouos} \\ $$

Question Number 73566 Answers: 0 Comments: 3

show that f(x) = ∣x∣ is not differentiable at x=0, where ∣x∣ denotes he absolute value function

$${show}\:{that}\:{f}\left({x}\right)\:=\:\mid{x}\mid\:{is}\:{not}\:{differentiable}\:{at}\:{x}=\mathrm{0},\:{where}\:\mid{x}\mid \\ $$$${denotes}\:{he}\:{absolute}\:{value}\:{function} \\ $$

Question Number 73565 Answers: 0 Comments: 2

investigate the continuity of f ,given by f: x → { ((1−x, if x<1)),((0,if x =1)),((x^2 −3x + 2,if x >1)) :} at the point x =1

$${investigate}\:{the}\:{continuity}\:{of}\:{f}\:,{given}\:{by} \\ $$$${f}:\:{x}\:\rightarrow\:\begin{cases}{\mathrm{1}−{x},\:{if}\:{x}<\mathrm{1}}\\{\mathrm{0},{if}\:{x}\:=\mathrm{1}}\\{{x}^{\mathrm{2}} −\mathrm{3}{x}\:+\:\mathrm{2},{if}\:{x}\:>\mathrm{1}}\end{cases} \\ $$$${at}\:{the}\:{point}\:{x}\:=\mathrm{1} \\ $$$$ \\ $$

Question Number 73561 Answers: 1 Comments: 0

find the value of λ for which f : x → { ((2λ − x, if x < 1)),((λ^2 + x −1, if x > 1)) :} has a limit as x→ 1

$${find}\:{the}\:{value}\:{of}\:\lambda\:{for}\:{which} \\ $$$$\:{f}\::\:{x}\:\rightarrow\:\begin{cases}{\mathrm{2}\lambda\:−\:{x},\:{if}\:{x}\:<\:\mathrm{1}}\\{\lambda^{\mathrm{2}} \:+\:{x}\:−\mathrm{1},\:{if}\:{x}\:>\:\mathrm{1}}\end{cases} \\ $$$${has}\:{a}\:{limit}\:{as}\:{x}\rightarrow\:\mathrm{1} \\ $$

Question Number 73560 Answers: 1 Comments: 1

prove that (1−itanθ)/(i+cotθ)=itanθ pleas sir help me?

$${prove}\:{that}\:\left(\mathrm{1}−{itan}\theta\right)/\left({i}+{cot}\theta\right)={itan}\theta \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$

Question Number 73555 Answers: 1 Comments: 4

find a) Lim_(x→−∞) ((ln(1+e^x ))/e^x ) b) lim_(x→+∞) ((√(x^2 + 3x)) −x) c) lim_(x→0) (√x) ln(sinx) d) lim_(x→+∞) ((e^(2x+1) −e^x )/(x^2 −x−1)) e) lim_(x→−∞) [(√(1−xe^x )) ]

$${find}\: \\ $$$$\left.{a}\right)\:\:\underset{{x}\rightarrow−\infty} {{Lim}}\:\frac{{ln}\left(\mathrm{1}+{e}^{{x}} \right)}{{e}^{{x}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow+\infty} {{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}}\:\:−{x}\right) \\ $$$$\left.{c}\right)\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\sqrt{{x}}\:{ln}\left({sinx}\right) \\ $$$$\left.{d}\right)\:\:\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{{e}^{\mathrm{2}{x}+\mathrm{1}} −{e}^{{x}} }{{x}^{\mathrm{2}} −{x}−\mathrm{1}} \\ $$$$\left.{e}\right)\:\underset{{x}\rightarrow−\infty} {{lim}}\left[\sqrt{\mathrm{1}−{xe}^{{x}} \:}\:\right] \\ $$

Question Number 73553 Answers: 1 Comments: 0

give: a,b,c>0 if a∣b and b∣c prove : a∣c

$$\mathrm{give}:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{if}\:\mathrm{a}\mid\mathrm{b}\:\mathrm{and}\:\mathrm{b}\mid\mathrm{c} \\ $$$$\mathrm{prove}\::\:\mathrm{a}\mid\mathrm{c} \\ $$

Question Number 73552 Answers: 1 Comments: 1

evaluate Lim_(x→+∞) xln (((x+1)/x))

$${evaluate}\: \\ $$$$\underset{{x}\rightarrow+\infty} {\:{Lim}}\:{xln}\:\left(\frac{{x}+\mathrm{1}}{{x}}\right) \\ $$

Question Number 73551 Answers: 1 Comments: 0

how many divisors does 38500 have?

$${how}\:{many}\:{divisors}\:{does}\:\mathrm{38500}\:{have}? \\ $$

Question Number 73550 Answers: 0 Comments: 0

solve 87x ≡ 3 (mod 5) and 55x ≡ 35 (mod 75)

$${solve}\: \\ $$$$\:\:\mathrm{87}{x}\:\equiv\:\mathrm{3}\:\left({mod}\:\mathrm{5}\right)\:{and} \\ $$$$\:\mathrm{55}{x}\:\equiv\:\mathrm{35}\:\left({mod}\:\mathrm{75}\right) \\ $$

Question Number 73545 Answers: 1 Comments: 2

evaluate ∫lnx dx

$${evaluate}\:\:\int{lnx}\:{dx} \\ $$

Question Number 73544 Answers: 1 Comments: 0

expressf(θ)= 8cosθ −15sinθ in the form rcos(θ + α), where r>0 and α is a positive acute angle hence find the general solution of the equation 80cos θ −150sinθ = 13 the maximum and minimum value of (5/(f(θ) + 3))

$${expressf}\left(\theta\right)=\:\mathrm{8}{cos}\theta\:−\mathrm{15}{sin}\theta\:{in}\:{the}\:{form} \\ $$$$\:{rcos}\left(\theta\:+\:\alpha\right),\:{where}\:{r}>\mathrm{0}\:{and}\:\alpha\:{is}\:{a}\:{positive}\:{acute}\:{angle} \\ $$$${hence} \\ $$$${find}\:{the}\:{general}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\:\:\mathrm{80}{cos}\:\theta\:−\mathrm{150}{sin}\theta\:=\:\mathrm{13} \\ $$$${the}\:{maximum}\:{and}\:{minimum}\:{value}\:{of}\:\:\frac{\mathrm{5}}{{f}\left(\theta\right)\:+\:\mathrm{3}} \\ $$

Question Number 73542 Answers: 0 Comments: 0

Given that the function f(x)= x^3 is differentiable in the interval (−2,2), Use the mean value theorem to find the value of x for which the tangent to the curve is parallel to the chord through the point (−2,8) and (2,8)

$${Given}\:{that}\:{the}\:{function}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} \:{is}\:{differentiable} \\ $$$${in}\:{the}\:{interval}\:\left(−\mathrm{2},\mathrm{2}\right),\:{Use}\:{the}\:{mean}\:{value}\:{theorem} \\ $$$${to}\:{find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$${is}\:{parallel}\:{to}\:{the}\:{chord}\:{through}\:{the}\:{point}\:\left(−\mathrm{2},\mathrm{8}\right)\:{and}\:\left(\mathrm{2},\mathrm{8}\right) \\ $$

Question Number 73538 Answers: 2 Comments: 0

find the general solution of sin4x + cos2x = 0

$${find}\:{the}\:{general}\:{solution}\:{of}\: \\ $$$$\:{sin}\mathrm{4}{x}\:+\:{cos}\mathrm{2}{x}\:=\:\mathrm{0} \\ $$

Question Number 73537 Answers: 1 Comments: 0

prove by induction that 4^n + 3^n +2 is a multiple of 3 ∀ n Z^+

$${prove}\:{by}\:{induction}\:{that}\:\mathrm{4}^{{n}} \:+\:\mathrm{3}^{{n}} \:+\mathrm{2}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{3} \\ $$$$\forall\:{n}\:{Z}^{+} \\ $$

Question Number 73536 Answers: 1 Comments: 0

prove that they are infinitely many primes

$${prove}\:{that}\:{they}\:{are}\:{infinitely}\:{many}\:{primes} \\ $$

Question Number 73530 Answers: 1 Comments: 0

given the 3^(rd) degree polynomial P(x) = (2x −1)(x−3)Q(x) + 12x−8 given that (x−1) is a factor of P(x) and P(0) = 10 find Q(x)