b) F1+ F3+ F, + . + F2n-1 d) Fn+k = FkFn+1+ Fk-1Fn; F2n; ...

Q: (m) For ro = -8, 11 = -7, 12 = -6, 13 = -5, I4 = -4, f(z1)Ar,

A: Given

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A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

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A: Consider the following equation: z=eax+byfax-by Differentiate z with respect to x taking y as a…

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A: To solve the integral, the formula of the "by parts of integration" will be used, that is,∫u v dx =…

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A: We have to solve the given system of equation by Cramer's rule

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A:

Q: Prove V²f(r) = d²f dr² + 2 df r dr

A:

Q: O max(x,z) О тах(хә 10xz + 3x + z suисh that 3 > 6х + 3z. О mincә 10xz+ 3x + z such that 3 6х + 3z

A:

Q: 2etūsw ER' such that and iov-2.Than (3ü)(B)

A:

Q: 25) of y' = = %3D 25 is 19

A:

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: 54, find r such that the m 5a. A -[ 3 -3 -2

A: A matrix 'A' is equal to its own inverse when  A2=I where I is the identity matrix.

Q: A = Acosx + Bsinx + 1 and B = -Asinx + Bcosx Then, what is the A, B ?

A: The detailed solution is given below  Thank you

Q: flt) = Ualt) U, It) (t -3)2 + o uslt) sinzlt-s)

A:

Q: Let FECT-2,21], foro. Prave that Max -2

A:

Q: a²u , a?u k x² ди at ax2 ' ay?, ||

A: In this question, we used the separation of the variable method to solve the 2-D heat flow.

Q: Is the equation Ax = b consistent for all b in R^3? Explain.

A:

Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: 1. P+Q, -Q v -P 2. P, (P v Q) v P 3. Pv Q, P --> Q, -Q^ -P 4. -P-->-Q, Q-->P

A: This is a multipart question having more than 1 interrelated subparts. As per company policy, we…

Q: Determine ar and y such that 4 -6] 4 2x + y [4 4 -4] x – y 0 -27 0 2 1 4 3

A: To determine the values of x and y.

Q: Let X=(1,0, – 1, - /2)'. Then, ||X||, =| Select one: а. -1- V3 b. -V3 O C. 2 +/2 d. -V2

A:

Q: B. Use Cramer's Rule to find the solution to 2x1 + x2 + x3 = 2x1 – 3x2 – 3x3 = 3 - - -2x1 – 2x2 +…

A:

Q: A² Show that w'= -9-7x - 15x² can be written as the Linear combination of U= 2 + x +4x²₁ V = 1 =…

A: Given that W'=-9-7x-15x2. Show that the given equation  can be written as the linear combination of…

Q: C) = ("; ')-(,",) n Q1. Show that : r

A: R.H.S;=n+1r-nr-1=(n+1)!r! (n+1-r)!-n!(r-1)! (n-r+1)!=1 (n+1-r)!(n+1) n!r(r-1)!-n!(r-1)!=n!…

Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

A:

Q: ax + by + cz + dq = 0 ,ax + by + cz + d2 %3D

A:

Q: Solve the following IBVP: Utt = 4uzz 0 0, u, (0, t) = u,(27, t) = 0, t>0, u(x,0) = 0, 0<I< 2n, T.…

A:

Q: 2. If AWXY~AVTU find the measure of ZT. W (2r-2) (8x- 7) Y (3r - 6)

A: Given  ∆WXY~∆VTU To find ∠T

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A:

Q: Disprove: X={r1, 12} iff V, (z E X +x=VI=T2)

A: To do: Disprove the statement…

Q: Show that e 12-1/31 2+3az| 2re?

A: The given inequality is                                           ∮|z-1|=1ezz+3dz≤2πe2 To prove the…

Q: 25. If ā = -j and b = 2x +5y, express and y in terms of ā and b.

A:

Q: Show that if 0 <y<1, and Y ~ N(0,1), we have that 9 6 3 P\Y + %(x² – 1) < =] × + (V +1). -

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 4. Verify that (¹)² (j³)² = j³² | j³² but (²)³ #jj² j2

A:

Q: Express by ¡y; in the terms of x variables where y; = C¡¡x; and bicik = 8k.

A: Given equations as yi=cijxj and bijcik=δki

Q: 51 3 -[---] -4 2 -2 Let u= (a) 5u-2v, 3 V= 5 W= -1 Find:

A:

Q: Let X=(1,0, – 1,- /2)'. Then, ||X||, = Select one: а. -V3 O . 2+V2 C. -V2

A:

Q: what is convolution of [(e^-2t)u(t)]*3dirac(t)+6e^-2t

A:

Q: Show that: If Iz| = 1, then: %3D z3 + 4z? – 4| Im < 3 z + 4

A: Since |z|=1 Let z=r(cos∅+isin∅) ⇒|r(cos∅+isin∅)|=1 ⇒r=1 Now

Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

A:

Q: 8. So dt V5+r²

A:

Q: JJ. JUA X ABD) 224 ABE) 16 36. g(x)=2x -3x² +5x+3 ACD) 1 АCE) 2 37. h(x)=x -4x³ +3x² +8 ADE) -3 BCD)…

A:

Q: Find Ai シ+ト+トz= \ + 0,5A-0-がアr ー /3

A: To find A1 and A2 from the given two equations

Q: fx, x, (*1 *2) = 16 1X¡l < 4, 2 < X2 < 4 are independent and orthogonal.

A:

Q: Find the pointP such that v = PQ has the components (-9.75, 5.75, – 16.5). Q = (-7.75, 6.75, –9.5)…

A:

Q: +prove by indirect method that i X+y >5 then or y>3. x>2

A: We need to prove that if x+y&gt;5 then x&gt;2 or y&gt;3

Q: 1) y = a², from P(-1,,) to Q(1,;) .2 1 2) x = 3VI(y – 3), 1 <y<2 - 3

A: We have to find the arc length of given curve

Q: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one

Q: Assume x, y, z E R³. and x · y= x · z = y• z = 0. If ||æ|| = 3, ||y|| = 12, ||2|| = 4, what is || –…

A: A correct

Q: a,b,x,y, are negative numbers a⁵ + b⁵<= 1 x⁵ + y⁵ <= 1 prove that a²x³ + b²y³ <= 1

A: Given information: The numbers a,b,x and y are negative numbers. The conditions are a5+b5≤1,…

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.