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Question Number 201464 Answers: 2 Comments: 0

if f(2) = 3 and f(4) = 5 find ∫_2 ^( 4) f(x) ∙ f^′ (x) dx = ?

$$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:\mathrm{3}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{4}\right)\:=\:\mathrm{5} \\ $$$$\mathrm{find}\:\:\:\int_{\mathrm{2}} ^{\:\mathrm{4}} \:\mathrm{f}\left(\mathrm{x}\right)\:\centerdot\:\mathrm{f}\:^{'} \left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 201441 Answers: 1 Comments: 0

Let f(x) and g(x) be given by f(x)= (1/x) +(1/(x−2)) +(1/(x−4)) + ... +(1/(x−2018)) and g(x)=(1/(x−1)) +(1/(x−3)) +(1/(x−5)) +...+ (1/(x−2017)). Prove that ∣ f(x)−g(x)∣ >2 for any non−integer real number x satisfying 0<x<2018.

$${Let}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{be}\:{given}\:{by}\: \\ $$$$\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{x}−\mathrm{2}}\:+\frac{\mathrm{1}}{{x}−\mathrm{4}}\:+\:...\:+\frac{\mathrm{1}}{{x}−\mathrm{2018}} \\ $$$$\:{and}\: \\ $$$$\:\:{g}\left({x}\right)=\frac{\mathrm{1}}{{x}−\mathrm{1}}\:+\frac{\mathrm{1}}{{x}−\mathrm{3}}\:+\frac{\mathrm{1}}{{x}−\mathrm{5}}\:+...+\:\frac{\mathrm{1}}{{x}−\mathrm{2017}}. \\ $$$$\:\:{Prove}\:{that}\:\:\mid\:{f}\left({x}\right)−{g}\left({x}\right)\mid\:>\mathrm{2} \\ $$$$\:\:{for}\:{any}\:{non}−{integer}\:{real}\:{number} \\ $$$$\:\:{x}\:{satisfying}\:\mathrm{0}<{x}<\mathrm{2018}.\: \\ $$

Question Number 201430 Answers: 1 Comments: 0

Find: (2/(35)) + (2/(63)) + (2/(99)) + (2/(143)) = ?

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{2}}{\mathrm{35}}\:+\:\frac{\mathrm{2}}{\mathrm{63}}\:+\:\frac{\mathrm{2}}{\mathrm{99}}\:+\:\frac{\mathrm{2}}{\mathrm{143}}\:=\:? \\ $$

Question Number 201408 Answers: 3 Comments: 0

Question Number 201388 Answers: 2 Comments: 0

Question Number 201343 Answers: 1 Comments: 0

Question Number 201463 Answers: 1 Comments: 0

a = constant number: if ∫x ∙ f(x) dx = x^3 - x^2 + 4x - (a/5) find f(2) = ?

$$\mathrm{a}\:=\:\mathrm{constant}\:\mathrm{number}: \\ $$$$\mathrm{if}\:\:\:\int\mathrm{x}\:\centerdot\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:-\:\frac{\mathrm{a}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 201462 Answers: 1 Comments: 0

Find: ∫_0 ^( 𝛑) (√(1 - 4 sin^2 (x/2) cos^2 (x/2))) dx = ?

$$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \:\sqrt{\mathrm{1}\:-\:\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{cos}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 201460 Answers: 0 Comments: 0

Find the smallest positive period of the function: y = ∣ tan 2x ∣ + ∣ cot 2x ∣

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{function}: \\ $$$$\mathrm{y}\:=\:\mid\:\mathrm{tan}\:\mathrm{2x}\:\mid\:\:+\:\:\mid\:\mathrm{cot}\:\mathrm{2x}\:\mid \\ $$

Question Number 201302 Answers: 1 Comments: 0

{ ((x^2 + y^(−2) = 4)),((x^(−2) + y^2 = 5)) :} find: (y/x) = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{−\mathrm{2}} \:=\:\mathrm{4}}\\{\mathrm{x}^{−\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{5}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:? \\ $$

Question Number 201282 Answers: 1 Comments: 0

Question Number 201253 Answers: 2 Comments: 0

find the sum of n terms of the serice s_n =5+11+19+29+41+..........

$${find}\:{the}\:{sum}\:{of}\:{n}\:{terms}\:{of}\:{the}\:{serice} \\ $$$${s}_{{n}} =\mathrm{5}+\mathrm{11}+\mathrm{19}+\mathrm{29}+\mathrm{41}+.......... \\ $$

Question Number 201237 Answers: 1 Comments: 3

If , a ∣ 5b^( 2) −10b +1 ⇒ [ a , 5b ]_(lcm) = ?

$$ \\ $$$$\:\:\:\:{If}\:\:,\:\:\:{a}\:\mid\:\mathrm{5}{b}^{\:\mathrm{2}} −\mathrm{10}{b}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\Rightarrow\:\:\:\left[\:{a}\:\:,\:\mathrm{5}{b}\:\right]_{\mathrm{lc}{m}} \:=\:\:?\: \\ $$$$ \\ $$$$ \\ $$

Question Number 201200 Answers: 3 Comments: 2

Question Number 201190 Answers: 1 Comments: 0

Question Number 201162 Answers: 4 Comments: 0

Question Number 201152 Answers: 4 Comments: 0

if 4^x +4^(−x) =7 then 8^x +8^(−x) =?

$${if}\:\:\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} =\mathrm{7} \\ $$$${then}\:\:\:\mathrm{8}^{{x}} +\mathrm{8}^{−{x}} =? \\ $$

Question Number 201149 Answers: 1 Comments: 0

Question Number 201106 Answers: 1 Comments: 0

calculate ... Σ_(n=1) ^∞ (( ζ(2n ))/(2^( n) .n)) = ?

$$ \\ $$$$\:\:\:\:\:{calculate}\:... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\left(\mathrm{2}{n}\:\right)}{\mathrm{2}^{\:{n}} .{n}}\:=\:? \\ $$$$ \\ $$

Question Number 201081 Answers: 4 Comments: 0

Question Number 201047 Answers: 0 Comments: 0

Question Number 201041 Answers: 1 Comments: 0

4(33)7 4(24)6 5( ? )4 a)9 b)18 c)27 d)36

$$\mathrm{4}\left(\mathrm{33}\right)\mathrm{7} \\ $$$$\mathrm{4}\left(\mathrm{24}\right)\mathrm{6} \\ $$$$\mathrm{5}\left(\:?\:\right)\mathrm{4} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\:\:\:\:\:{b}\right)\mathrm{18}\:\:\:\:\:{c}\right)\mathrm{27}\:\:\:\:\:{d}\right)\mathrm{36} \\ $$

Question Number 201034 Answers: 0 Comments: 0

Question Number 200971 Answers: 1 Comments: 0

Question Number 200961 Answers: 2 Comments: 0

−x^3 +1=((−x+1))^(1/3) ⇒x=?

$$\: \\ $$$$\:\:\:\:\:−{x}^{\mathrm{3}} +\mathrm{1}=\sqrt[{\mathrm{3}}]{−{x}+\mathrm{1}}\:\Rightarrow{x}=? \\ $$$$ \\ $$

Question Number 200937 Answers: 2 Comments: 0

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