Prove that x3 x7

Q: IsP2 spanned by 1 + x, x + x2,1 + x2?

A: To Show: Is P2 spanned by 1+x,  x+x2, 1+x2 ? Concept: Let V be a vector space and let S=v1, v2, v3,…

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

A:

Q: Prove that 1+1=2

A: To prove: 1 + 1 = 2

Q: Differentiate the following powers of x. 1/x4

A: y=1x4⇒y=x-4

Q: Prove that (3-2)(x+2) = 3+2i ifitues.

A:

Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: Prove that 1. 1. 1 + 1x 2'2x 3 1 = 1 – (п — 1) хп + 3 x 4

A:

Q: Prove that (A-1)-1 = A. %3|

A: Let A be inverse of matrix A. Then, by definition We know that

Q: Prove that Σ = 2" . a. x=0 b. = 0. x=0

A:

Q: Prove that x2 + 3x + 3 > 0 for all x.

A:

Q: Prove that x4 + 15x3 + 7 is irreducible over Q

A:

Q: Show that п ()- = 1- 1 and п,

A: It is given that,

Q: _x) = -(x + 4)(x – 2)(x

A:

Q: all real x, is X.

A:

Q: PROVE that 2a + b = 0.

A:

Q: Prove that if x2+2 is even then x is even

A: We know that even number can be expressed as 2k where k is an integer . Or other words every even…

Q: Prove that there are integers x and y such that 10x-13y=1

A:

Q: Show that 1+1/x+1/x2+1/x3+1/x4+…=x / x−1 assuming x>1.

A:

Q: Prove that x2 + 3x + 3 ≥ 0 for all x.

A: We have been given the quadratic equation  x2+3x+3

Q: Let à . Find al.

A:

Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

A:

Q: Prove by contraposition that if x^5 + 7x^3 + 5x >= x^4 + x^2 +8, then x >= 0

A: Proof using contraposition: If we want to prove "if A, then B", then using contrapositive statement…

Q: : Prove that [ X" Ju Cx]=x* Ju-l X)

A:

Q: Prove that ax² bx C + + (x − a) (x −b) (x −c) (x-b) (x-c) x-c -+1 x³ 3 (x-a)(x-b)(x-c)

A:

Q: Show that  ℝ2 = span([1 1], [1 -1])

A:

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: Show that f(x)= = x³+2x-4 4x²-5 is O(x).

A:

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: Prove that: ā x (B x č) = (ã-č )b – (ã ·5 )ẽ

A: See the details solution in below

Q: Prove that =0

A: ∑i=0ne-λλxx!=1n!∫λ∞ e-xxn    ...............(1) We will proof this by using induction on n. Here,…

Q: Suppose that 0 <ƒ′(x) < 1/2 for all x-values. Show that ƒ(-1) < ƒ(1) < 2 + ƒ(-1)

A: From the given inequality the behaviour of the function can be determined as.

Q: L) Prove that (3-2)(x+2) = 3 +21 iFitwas

A:

Q: Prove that x + 3 is odd if and only if x² is even.

A: Proof: x+3 is odd  Let x+3 = 2k+1

Q: Prove that √2 is not an element of Q(?).

A:

Q: Find the coefficient of x in (1+x'+x°).

A:

Q: Prove that x=0(x)

A: We say that a function f is O(g) if there exist constants M and C>0 such that For all x>M…

Q: n Show that (") = (,“,) n-r.

A:

Q: Show that lGl =20 , so G is not simple

A:

Q: Prove that F (3x)(A → B) → ()A → (3x)B.

A: We have to prove, ∃xA→B→∀xA→∃xB

Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

Q: Find (a) if fx) = /x-a+1.

A:

Q: Differentiate the following powers of x. x3

A: Differentiate the following powers of x. x3

Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

A:

Q: If x^3+1/x^3=18√3 prove that:1/x=√3-√2

A: Given,            x3 + 1x3=183

Q: Let ā . Find |ā].

A:

Q: 6x-C), Prove that If2zf(x+ct)+Ø て

A:

Q: Frngl. prove that x

A:

Q: Prove that le-2z| 0.

A:

Q: Prove that: ā x (B xẽ) = (ã č)b – (ā-B )ë |

A: We have to prove that a→×b→×c→=a→⋅c→b→−a→⋅b→c→. Let a→=a1i^+a2j^+a3k^ b→=b1i^+b2j^+b3k^ And…

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.