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AllQuestion and Answers: Page 232

Question Number 192793 Answers: 2 Comments: 0

x^4 +x^3 +x^2 +x+1=y^2 where y is positive integer number then find the positive integal values of (x) for which that holds

$x^{4} + x^{3} + x^{2} + x + 1 = y^{2} w h e r e y i s p o s i t i v e i n t e g e r n u m b e r$ $t h e n f i n d t h e p o s i t i v e i n t e g a l v a l u e s o f (x)$ $f o r w h i c h t h a t h o l d s$

Question Number 192791 Answers: 1 Comments: 0

If n is a positive integer, prove that 2^n Γ(n+(1/2)) = 1.3.5...(2n−1)(√π). Help!

$If n is a positive integer, prove that$ $2^{n} Γ (n + \frac{1}{2}) = 1.3.5 . . . (2 n - 1) \sqrt{π} .$ $Help!$

Question Number 192786 Answers: 1 Comments: 0

N=<aabb>∈N & N is perfect square find N ?

$N =< a a b b >\in N & N i s p e r f e c t s q u a r e$ $f i n d N ?$

Question Number 192780 Answers: 1 Comments: 1

Question Number 192770 Answers: 1 Comments: 4

Question Number 192766 Answers: 0 Comments: 0

if π/2<x<π and (√(1+sin x/1−sin x= ksec x ,then k=))

$i f π / 2 < x < π a n d \sqrt{1 + \sin x / 1 - \sin x = k \sec x, t h e n k =}$

Question Number 192765 Answers: 1 Comments: 0

Question Number 192763 Answers: 1 Comments: 0

Prove that: sin A + sin B + sin C > 2 (A,B,C ∈ (π/2))

$P r o v e t h a t :$ $s i n A + s i n B + s i n C > 2$ $(A, B, C \in \frac{π}{2})$

Question Number 192758 Answers: 3 Comments: 0

what is the value of dy/dx if y = cot^(−1) [(((√(1+sinx))+(√(1−sinx)))/( (√(1+sinx))−(√(1−sinx))))]; x∈(0,(π/2)) please give complete explanation that why can we not take [sinx/2−cosx/2]^2 = 1−sinx

$w h a t i s t h e v a l u e o f d y / d x i f$ $y = {c o t}^{- 1} [\frac{\sqrt{1 + s i n x} + \sqrt{1 - s i n x}}{\sqrt{1 + s i n x} - \sqrt{1 - s i n x}}]; x \in (0, \frac{π}{2})$ $p l e a s e g i v e c o m p l e t e e x p l a n a t i o n t h a t$ $w h y c a n w e n o t t a k e$ ${[s i n x / 2 - c o s x / 2]}^{2} = 1 - s i n x$

Question Number 192756 Answers: 1 Comments: 1

Question Number 192777 Answers: 0 Comments: 2

(√(x^2 +ax−1))−(√(x^2 +bx−1))=(√a)−(√b) find x .

$\sqrt{x^{2} + a x - 1} - \sqrt{x^{2} + b x - 1} = \sqrt{a} - \sqrt{b}$ $f i n d x .$

Question Number 192746 Answers: 1 Comments: 0

Let G be the group ({1, ı, −1, −ı}, ∙) and let H ≤ (+_− 1, ∙), show that θ:G→H is an Isomorphism. Hello!

$Let G be the group ({1, ı, - 1, - ı}, \cdot)$ $and let H ⩽ (\underline{+} 1, \cdot), show that$ $θ : G \to H is an Isomorphism .$ $Hello!$

Question Number 192743 Answers: 1 Comments: 0

Calculate: I=∫_0 ^( 4) (∫_(x−4) ^( x−2) e^((x+y)/(x−y)) dy)dx

$C a l c u l a t e :$ $I = \int_{0}^{4} (\int_{x - 4}^{x - 2} e^{\frac{x + y}{x - y}} d y) d x$

Question Number 192738 Answers: 2 Comments: 0

Find the supremum and infimum of each of the following sequence a) {((n−1)/(2n))} b) {(((−)^n n)/(2n+1))} c){((1+(−)^n )/3)} d) {sin((nπ)/2)} e) {(1/n) − sin((nπ)/2)} f) {(1+(1/(2n)))cos((nπ)/3)} Help!

$Find the supremum and infimum$ $of each of the following sequence$ $a) {\frac{n - 1}{2 n}} b) {\frac{{(-)}^{n} n}{2 n + 1}} c) {\frac{1 + {(-)}^{n}}{3}}$ $d) {\sin \frac{n π}{2}} e) {\frac{1}{n} - \sin \frac{n π}{2}}$ $f) {(1 + \frac{1}{2 n}) \cos \frac{n π}{3}}$ $Help!$