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Question Number 25279 Answers: 2 Comments: 0

Find the domain and range of f(x)=(√((((x−5)/(x−3)))))

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\sqrt{\left(\frac{{x}−\mathrm{5}}{{x}−\mathrm{3}}\right)} \\ $$

Question Number 25237 Answers: 0 Comments: 1

prooove that 0!=1

$${prooove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 25236 Answers: 0 Comments: 1

Question Number 25230 Answers: 1 Comments: 0

Let X is natural number . Multification of its digits is X^2 − 97X + 2020 . Find the value of X_(maximum) + X_(minimum) .

$${Let}\:\:{X}\:\:{is}\:{natural}\:\:{number}\:. \\ $$$${Multification}\:\:{of}\:\:{its}\:\:{digits}\:\:{is}\:\:{X}^{\mathrm{2}} \:−\:\mathrm{97}{X}\:+\:\mathrm{2020}\:. \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{X}_{{maximum}} \:\:+\:\:{X}_{{minimum}} \:\:. \\ $$

Question Number 25229 Answers: 0 Comments: 1

∫(1/(√(x^2 +1)))dx

$$\int\frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$

Question Number 25224 Answers: 1 Comments: 0

∫(2x−1)(√(x×x−x+1 dx))

$$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}×{x}−{x}+\mathrm{1}\:\:\:{dx}} \\ $$

Question Number 25226 Answers: 1 Comments: 0

Show that if x=3−(√3).Show that x^2 +((36)/x^2 )=24

$${Show}\:{that}\:{if}\:{x}=\mathrm{3}−\sqrt{\mathrm{3}}.{Show}\:{that}\:{x}^{\mathrm{2}} +\frac{\mathrm{36}}{{x}^{\mathrm{2}} }=\mathrm{24} \\ $$

Question Number 25221 Answers: 1 Comments: 0

Find the lim_(x→∞) (e^x /(√(e^(2x) +1)))

$$\mathrm{Find}\:\mathrm{the}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{e}^{\mathrm{x}} }{\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}} \\ $$

Question Number 25215 Answers: 0 Comments: 1

Question Number 25209 Answers: 1 Comments: 0

∫cosec(√(4x^2 ))dx

$$\int{cosec}\sqrt{\mathrm{4}{x}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$

Question Number 25203 Answers: 1 Comments: 1

Question Number 25201 Answers: 1 Comments: 0

Question Number 25200 Answers: 1 Comments: 0

The point A has coordinate (− 1, − 5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x − axis at C and the y − axis at D. Calculate the length of CD

$$\mathrm{The}\:\mathrm{point}\:\mathrm{A}\:\mathrm{has}\:\mathrm{coordinate}\:\left(−\:\mathrm{1},\:\:−\:\mathrm{5}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{point}\:\mathrm{B}\:\mathrm{has}\:\mathrm{coordinates}\:\left(\mathrm{7},\:\mathrm{1}\right). \\ $$$$\mathrm{The}\:\mathrm{perpendicular}\:\mathrm{bisector}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{meets}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis}\:\mathrm{at}\:\mathrm{C}\:\mathrm{and}\:\mathrm{the}\:\mathrm{y}\:−\:\mathrm{axis}\:\mathrm{at} \\ $$$$\mathrm{D}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{CD} \\ $$

Question Number 25199 Answers: 1 Comments: 1

A line has equation y = 2x − 7 and a curve has equation y = x^2 − 4x + c, where c is a constant. Find the set of possible values of c for which the line does not intersect the curve.

$$\mathrm{A}\:\mathrm{line}\:\mathrm{has}\:\mathrm{equation}\:\mathrm{y}\:=\:\mathrm{2x}\:−\:\mathrm{7}\:\mathrm{and}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{has}\:\mathrm{equation}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{c}, \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{c}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{intersect}\:\mathrm{the}\:\mathrm{curve}. \\ $$

Question Number 25198 Answers: 0 Comments: 0

Given sin (K + L) cos M = 2 sin K cos (L − M) Prove that tan M = ((sin (L − K))/(2 sin K sin L))

$$\mathrm{Given} \\ $$$$\mathrm{sin}\:\left({K}\:+\:{L}\right)\:\mathrm{cos}\:{M}\:=\:\mathrm{2}\:\mathrm{sin}\:{K}\:\mathrm{cos}\:\left({L}\:−\:{M}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan}\:{M}\:=\:\frac{\mathrm{sin}\:\left({L}\:−\:{K}\right)}{\mathrm{2}\:\mathrm{sin}\:{K}\:\mathrm{sin}\:{L}} \\ $$

Question Number 25191 Answers: 0 Comments: 3

A man is climbing a ladder which is inclined to the wall at an angle of 30° . If he ascends at a rate of 2 m/s then he approaches the wall at the rate of−

$$\mathrm{A}\:\mathrm{man}\:\mathrm{is}\:\mathrm{climbing}\:\mathrm{a}\:\mathrm{ladder}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{inclined}\:\mathrm{to}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°\:. \\ $$$$\mathrm{If}\:\mathrm{he}\:\mathrm{ascends}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{2}\:\mathrm{m}/\mathrm{s}\:\mathrm{then}\: \\ $$$$\mathrm{he}\:\mathrm{approaches}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}− \\ $$$$ \\ $$

Question Number 25188 Answers: 0 Comments: 1

the straight line x+y=0 3x+y−4i=0 and x+3y−4=0 forms a triangle which triangle it is

$${the}\:{straight}\:{line}\:{x}+{y}=\mathrm{0}\:\: \\ $$$$\mathrm{3}{x}+{y}−\mathrm{4}{i}=\mathrm{0} \\ $$$${and}\:{x}+\mathrm{3}{y}−\mathrm{4}=\mathrm{0}\:{forms}\:{a}\:{triangle}\:{which}\:{triangle}\: \\ $$$${it}\:{is} \\ $$

Question Number 25187 Answers: 0 Comments: 1

if in a quadratic eqution x^2 +ax+b=0 and x^2 +bx+a=0 have a common root then the numerical value of (a+b) is

$${if}\:{in}\:{a}\:{quadratic}\:{eqution}\:{x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0} \\ $$$${and}\:{x}^{\mathrm{2}} +{bx}+{a}=\mathrm{0}\:{have}\:{a}\:{common}\:{root} \\ $$$${then}\:{the}\:{numerical}\:{value}\:{of}\:\left({a}+{b}\right)\:{is} \\ $$

Question Number 25184 Answers: 1 Comments: 1

if a and b are the root of the quadratic equation x^2 +2x+3 then find the value of α^2 /β+β^2 /α

$${if}\:{a}\:{and}\:{b}\:{are}\:{the}\:{root}\:{of}\:{the}\:{quadratic}\:{equation}\:{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}\:{then}\:{find}\:{the}\:{value}\:{of}\:\alpha^{\mathrm{2}} /\beta+\beta^{\mathrm{2}} /\alpha \\ $$

Question Number 25183 Answers: 0 Comments: 1

Prove that ∫_0 ^( ∞) ((x^6 dx)/((a^4 +x^4 )^2 ))= ((3π(√2))/(16a)) , (a>0) .