Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1544

Question Number 55748 Answers: 1 Comments: 1

Question Number 55737 Answers: 1 Comments: 2

Question Number 55736 Answers: 1 Comments: 0

Question Number 55735 Answers: 1 Comments: 0

Question Number 55733 Answers: 0 Comments: 1

Question Number 55725 Answers: 1 Comments: 0

Question Number 55724 Answers: 0 Comments: 4

Question Number 55707 Answers: 0 Comments: 0

Question Number 55706 Answers: 0 Comments: 0

Question Number 55705 Answers: 0 Comments: 0

Question Number 55704 Answers: 1 Comments: 0

Prove that: 2 sin (1/2)θcos (3/2)θ+2sin (5/2)θ +2 sin (3/2)θ+2sin (3/2)θcos (7/2)θ =sin 4θ+sin 5θ

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{2}\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}\theta\mathrm{cos}\:\frac{\mathrm{3}}{\mathrm{2}}\theta+\mathrm{2sin}\:\frac{\mathrm{5}}{\mathrm{2}}\theta\: \\ $$$$+\mathrm{2}\:\mathrm{sin}\:\frac{\mathrm{3}}{\mathrm{2}}\theta+\mathrm{2sin}\:\frac{\mathrm{3}}{\mathrm{2}}\theta\mathrm{cos}\:\frac{\mathrm{7}}{\mathrm{2}}\theta \\ $$$$=\mathrm{sin}\:\mathrm{4}\theta+\mathrm{sin}\:\mathrm{5}\theta \\ $$

Question Number 55702 Answers: 0 Comments: 5

s=∫_0 ^( x) (√(1+(3t^2 +p)^2 ))dt = ? take p=1 for a special case.

$${s}=\int_{\mathrm{0}} ^{\:{x}} \sqrt{\mathrm{1}+\left(\mathrm{3}{t}^{\mathrm{2}} +{p}\right)^{\mathrm{2}} }{dt}\:\:=\:? \\ $$$$\:\:\:\:{take}\:{p}=\mathrm{1}\:\:{for}\:{a}\:{special}\:{case}. \\ $$

Question Number 55701 Answers: 1 Comments: 1

Is true or not that 4181 is the only one Fibonacci′s number with no prime factor which is also a Fibonacci′s number?

$${Is}\:{true}\:{or}\:{not}\:{that}\:\mathrm{4181}\:{is}\:{the}\:{only}\:{one} \\ $$$${Fibonacci}'{s}\:{number}\:{with}\:{no}\:{prime}\:{factor} \\ $$$${which}\:{is}\:{also}\:{a}\:{Fibonacci}'{s}\:{number}? \\ $$

Question Number 55685 Answers: 1 Comments: 0

proof that Σ_(i=1) ^n (a_i /(a_i −x))=2015 has exactly n real roots.o<a_1 ....<a_n

$${proof}\:{that}\: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{a}_{{i}} }{{a}_{{i}} −{x}}=\mathrm{2015}\:{has}\:{exactly}\:{n}\:{real}\: \\ $$$${roots}.{o}<{a}_{\mathrm{1}} ....<{a}_{{n}} \\ $$

Question Number 55675 Answers: 0 Comments: 0

Question Number 55674 Answers: 1 Comments: 0

The smallest integer numbers with n ≥ 2018 so ((√3)+3i)^n form real numbers is..

$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{integer}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:{n}\:\geqslant\:\mathrm{2018}\:\mathrm{so} \\ $$$$\left(\sqrt{\mathrm{3}}+\mathrm{3}{i}\right)^{{n}} \:\mathrm{form}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{is}.. \\ $$

Question Number 55673 Answers: 0 Comments: 0

f(z)=z Re(z)+z^ Im(z) +z^ f′(z_0 )=...

$${f}\left({z}\right)={z}\:\mathrm{Re}\left({z}\right)+\bar {{z}}\:\mathrm{Im}\left({z}\right)\:+\bar {{z}}\: \\ $$$${f}'\left({z}_{\mathrm{0}} \right)=... \\ $$

Question Number 55672 Answers: 0 Comments: 0

The value of complex integral ∫_(∣z∣=1) (z^2 sin (1/z)+(1/z^2 )sin z) dz is...

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{\mid{z}\mid=\mathrm{1}} \left({z}^{\mathrm{2}} \mathrm{sin}\:\frac{\mathrm{1}}{{z}}+\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\mathrm{sin}\:{z}\right)\:{dz}\:\mathrm{is}... \\ $$

Question Number 55671 Answers: 0 Comments: 0

Let z ∈ C , so ∣1+z^2 ∣<1. Prove that 2∣1+z^2 ∣≥1

$$\mathrm{Let}\:\mathrm{z}\:\in\:\mathbb{C}\:,\:\mathrm{so}\:\mid\mathrm{1}+{z}^{\mathrm{2}} \mid<\mathrm{1}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}\mid\mathrm{1}+{z}^{\mathrm{2}} \mid\geqslant\mathrm{1} \\ $$

Question Number 55669 Answers: 0 Comments: 0

Question Number 55668 Answers: 1 Comments: 3

Find all functions y=f(x) such that y′y′′=y′′′.

$${Find}\:{all}\:{functions}\:{y}={f}\left({x}\right)\:{such}\:{that} \\ $$$${y}'{y}''={y}'''. \\ $$

Question Number 55666 Answers: 0 Comments: 0

Question Number 55665 Answers: 0 Comments: 0

Question Number 55663 Answers: 2 Comments: 0

Question Number 55658 Answers: 1 Comments: 0

find the difference of the roots of the following quadratic equation (3+2(√(2 )))x^2 +(1+(√2))x =2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}\:}\right)\mathrm{x}^{\mathrm{2}} \:+\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\mathrm{x}\:=\mathrm{2} \\ $$

Question Number 55643 Answers: 0 Comments: 1

known function f diferensiable continues at [a, b] If f(a)=f(b)=0 and ∫_a ^b [f(x)]^2 dx=1 Prove that ∫_a ^b x^2 [f′(x)]^2 dx ≥(1/4)

$$\mathrm{known}\:\mathrm{function}\:{f} \\ $$$$\mathrm{diferensiable}\:\mathrm{continues}\:\mathrm{at}\:\left[{a},\:{b}\right] \\ $$$$\mathrm{If}\:{f}\left({a}\right)={f}\left({b}\right)=\mathrm{0} \\ $$$$\mathrm{and}\: \\ $$$$\int_{{a}} ^{{b}} \left[{f}\left({x}\right)\right]^{\mathrm{2}} {dx}=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\int_{{a}} ^{{b}} {x}^{\mathrm{2}} \left[{f}'\left({x}\right)\right]^{\mathrm{2}} \:{dx}\:\geqslant\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Pg 1539 Pg 1540 Pg 1541 Pg 1542 Pg 1543 Pg 1544 Pg 1545 Pg 1546 Pg 1547 Pg 1548

Contact: info@tinkutara.com