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AllQuestion and Answers: Page 1343

Question Number 78682 Answers: 0 Comments: 2

Question Number 78667 Answers: 1 Comments: 0

let f(x)=(x+1)(((x+1)(x−3)^2 )/((x−1)^2 (x−4) )) then a. find x and y intercepts b. find vertical asymptote and horizontal asymtote c. find domain and range of f d. draw the graph of f

$${let}\:{f}\left({x}\right)=\left({x}+\mathrm{1}\right)\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} }{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{4}\right)\:}\:{then} \\ $$$${a}.\:{find}\:{x}\:{and}\:{y}\:{intercepts} \\ $$$${b}.\:{find}\:{vertical}\:{asymptote}\:{and}\:{horizontal}\:{asymtote} \\ $$$${c}.\:{find}\:{domain}\:{and}\:{range}\:{of}\:{f} \\ $$$${d}.\:{draw}\:{the}\:{graph}\:{of}\:{f} \\ $$

Question Number 78694 Answers: 6 Comments: 2

Solve the equation. x^2 − (y − z)^2 = 10 ... (i) y^2 − (z − x)^2 = 5 ... (ii) z^2 − (x − y)^2 = 2 ... (iii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:−\:\left(\mathrm{y}\:−\:\mathrm{z}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{10}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\mathrm{y}^{\mathrm{2}} \:−\:\left(\mathrm{z}\:−\:\mathrm{x}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{5}\:\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\mathrm{z}^{\mathrm{2}} \:−\:\left(\mathrm{x}\:\:−\:\mathrm{y}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{2}\:\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 78693 Answers: 1 Comments: 3

Question Number 78655 Answers: 1 Comments: 2

Question Number 78652 Answers: 1 Comments: 0

Question Number 78650 Answers: 2 Comments: 4

Question Number 78643 Answers: 0 Comments: 2

sin 20×sin 40×sin 80=(√(3/8))

$$\mathrm{sin}\:\mathrm{20}×\mathrm{sin}\:\mathrm{40}×\mathrm{sin}\:\mathrm{80}=\sqrt{\mathrm{3}/\mathrm{8}} \\ $$

Question Number 78635 Answers: 1 Comments: 8

Question Number 78627 Answers: 0 Comments: 0

explicite f(x)=∫_(−∞) ^(+∞) ((arctan(xt +1))/(t^2 +x^2 ))dt with x>0

$${explicite}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({xt}\:+\mathrm{1}\right)}{{t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 78625 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((arctan(x^2 −3))/((x^2 +x+1)^2 ))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{3}\right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 78624 Answers: 0 Comments: 0

calculate ∫_0 ^(π/4) e^(−2x) ln(1+cosx)dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{cosx}\right){dx} \\ $$

Question Number 78623 Answers: 1 Comments: 0

calculate lim_(x→0) (((√(1+x+x^2 +....+x^n )) −1)/x^(n/2) )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} +....+{x}^{{n}} }\:\:−\mathrm{1}}{{x}^{\frac{{n}}{\mathrm{2}}} } \\ $$

Question Number 78622 Answers: 0 Comments: 1

calculate lim_(n→+∞) ∫_0 ^n (1−(t/n))^n ln(1+nt)dt

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} {ln}\left(\mathrm{1}+{nt}\right){dt} \\ $$

Question Number 78621 Answers: 0 Comments: 1

calculate lim_(x→1) ∫_x ^x^3 ((sh(xt^2 ))/(sin(xt)))dt

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\:\int_{{x}} ^{{x}^{\mathrm{3}} } \:\:\frac{{sh}\left({xt}^{\mathrm{2}} \right)}{{sin}\left({xt}\right)}{dt} \\ $$

Question Number 78620 Answers: 1 Comments: 0

explicit f(x) =∫_0 ^(+∞) ln(1−xe^(−t) )dt with ∣x∣<1

$${explicit}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} {ln}\left(\mathrm{1}−{xe}^{−{t}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 78609 Answers: 0 Comments: 0

Question Number 78628 Answers: 2 Comments: 1

Find minimum value of y = ((2x)/(x^2 + x + 1)) x , y ∈ R Without Differential

$${Find}\:\:{minimum}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\:{y}\:\:=\:\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{1}} \\ $$$${x}\:,\:{y}\:\:\in\:\:\mathbb{R} \\ $$$${Without}\:\:{Differential} \\ $$

Question Number 78596 Answers: 1 Comments: 1

lim_(x→0) (1−3tan^2 x)^((2/(sin^2 3x)) ) = ?

$$ \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{3tan}\:^{\mathrm{2}} \mathrm{x}\right)^{\frac{\mathrm{2}}{\mathrm{sin}\:^{\mathrm{2}} \:\mathrm{3x}}\:\:\:} =\:?\: \\ $$

Question Number 78581 Answers: 0 Comments: 4

∫ ((2xsin 2x)/((2x−sin 2x)^2 )) dx ?

$$\int\:\frac{\mathrm{2}{x}\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 78578 Answers: 0 Comments: 0

Question Number 78575 Answers: 1 Comments: 0

∫ (√(tan x)) dx

$$\int\:\sqrt{\mathrm{tan}\:\mathrm{x}}\:\:\mathrm{dx} \\ $$

Question Number 78569 Answers: 1 Comments: 0

which of the following is increasing or decreasing a. u_n = ((n!)/n^n ) b. u_n = (4^n /(3^n +1)) c. u_n = (2^n /n^2 )

$${which}\:{of}\:{the}\:{following}\:{is}\:{increasing}\:{or}\:{decreasing} \\ $$$${a}.\:\:{u}_{{n}} \:=\:\frac{{n}!}{{n}^{{n}} } \\ $$$${b}.\:\:{u}_{{n}} =\:\frac{\mathrm{4}^{{n}} }{\mathrm{3}^{{n}} +\mathrm{1}} \\ $$$${c}.\:{u}_{{n}} =\:\frac{\mathrm{2}^{{n}} }{{n}^{\mathrm{2}} } \\ $$

Question Number 78568 Answers: 1 Comments: 0

Find the roots of the equation bx^3 − (3b + 2)x^2 − 2(5b − 3)x + 20 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\mathrm{bx}^{\mathrm{3}} \:−\:\left(\mathrm{3b}\:+\:\mathrm{2}\right)\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2}\left(\mathrm{5b}\:−\:\mathrm{3}\right)\mathrm{x}\:+\:\mathrm{20}\:\:=\:\:\mathrm{0} \\ $$

Question Number 78567 Answers: 0 Comments: 9

Question Number 78564 Answers: 1 Comments: 1

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