Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) = s−rs, and solve for s.

Q: Determine the quotient and remainder if P(x)=x'+6x'+2x'+x-3 is divided by D(x)—x'—2х—1

A: Topic = Algebra

Q: Calculate s'(n) (8n + 5 s(n) = 2n-6/ 6

A: The given function is s(n)=8n+52n-66 To find the s'(n). Derivative formula:…

Q: dH f(5) = 8, f' (5) = 4 f(26) = 8, f'(26) = 6, g(5) = 1, g'(5) = -9, and H(x) = f(r² + g(x)). Find…

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Q: 47. If S(2,y)=(2x-3yy', then f,= _ a) -15(2x-3y)" b) –10(2x-3y) c) 15(2x-3y) d) 10(2x-3y)

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Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: 4y'''+12y''+13y'+10y=0

A:

Q: Find f. f(x) = f'(x) = −2+ 24x 12x², -x² + 4x³-x² + 14x+8 x - f(0) = 8, f'(0) = 12

A:

Q: Find B so that B^2 = A where A = 1 -1 0 -1 2 -1 0 -1 1

A:

Q: X(s)=(s^2+6s+7)/(s^2+3s+2) and Re{s}>-1 what is x(t)?

A: We are given : X(s)=s2+6s+7s2+3s+2 ⇒X(s)=s2+3s+2+3s+5s2+3s+2 ⇒X(s)=1+3s+5s2+3s+2 ---(1) Now,…

Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

A:

Q: E (3x(9 ^ b) V Jaæ(p ^ 0)) = 3x(p A (4 V 0))

A: To prove ⊢(∃x(φ∧ψ)∨∃x(φ∧θ))≡∃x(φ∧(ψ∨θ)) Here we have to use existential quantifiers i.e. notation of…

Q: 12 y' (12x +5) (4y* +3)° b. If y* +3y-4x' = 5x+1, then prove that y"(4y +3) = 24.x--

A:

Q: Zx-16zx+60z=e 5x

A: We can find the auxiliary equation and this easily find the general solution and then using the…

Q: Find dim(Q(a)), where

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Q: If X~BET(1,2) then E(X)= (1 2/B (1/B

A:

Q: If x' x= [(-₁)] and x(0) = [] x what is X(T)?

A: Given: x'=01-10x and x(0)=01. To find: x(π)

Q: The next iterative value of the root of (x^2)-4 using the Newton-Raphson method, if the initial…

A:

Q: 8. Find all the roots of f(x) =x* - 4x' + 6x² – 4x+5 if 2-iis one root.

A: Topic- roots of polynomial

Q: Fnd llull, lv , Uov, and d (4,v). (-1,7) , v- (1,9)

A: According to our company guidelines we are supposed to answer only first 3 sub parts. So here I'm…

Q: differentiate H with respect to G H-3e20G Select one: O a. H' = 60e 20G - 3/5G^(4/3) Ob. H' =…

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Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: I got to the step where I have (5h/h-1)/h. I think I can multimply (5h/h-1) by (h/1). This results…

A: We have to find actual expression for the given expression.

Q: Find the sum H=p+q+rand calculate average value of the function f(x),

A: In this question we have find the average value of function f(x) in the given interval. here we used…

Q: Compute the following. (a) Pa 4-

A: It is asked to find P9,4 C9,4 P10,10 C11,11

Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

A:

Q: Substitute the value of y' in 1 + (y)²

A:

Q: x) [in(3x²-36)]². Then f'(x) = A. 12x In (3x²-36) 3x²-36 O A. O B. O C. O D. O E. 2 In (3x²-36)…

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Q: f"(2) 1. Find

A: Given f(x)=43x2-23x+1f'(x)=-23*ddx(x)+43*ddx1x2+ddx(1)        =-2*13+4(-2)x-33+0

Q: A single bacterium divides every 0.5 hour to produce two complete bacteria. If we start with a…

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Q: L-1 { 10 / (S-2)(S2+1) }

A: Let  As-2+Bs+Cs2+1 = 10(s-2)(s2+1)A(s2+1)+(Bs+C)(s-2)(s-2)(s2+1) = 10(s-2)(s2+1)A(s2+1)+(Bs+C)(s-2)…

Q: Determine the value of 'k' if the L[ tk4t ] = 1/(s² - bs + 10).

A:

Q: 9. To solve L [et] = you may use: n! (s-a)n+1 [te] - (-1){(t)}

A: here , we need to find laplace transform of function f(t)= f     we know laplace transform of eat…

Q: Find f'(x). f(x) = (3x + 10)7 (1 − √) 3(3x + 10) (1 − √x)³ f'(x) = 21(3x + 10)6 (1-√) f'(x) = 7(3x +…

A: Given data÷ fx=3x+1071-x6 Find the first derivative f'x. Useful formula ddxxn=nxn-1…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.