3 show that x = x₁₂²₁ -X² is globally 4 2 asymptotically stable by using V(x) = — X ₁² + 1 X Can you show this by using V(x) = = 2 2² + 1 X ²2 ? 4 2 2

Q: 7. If f(r) = 6x³ - 5xª + 3z³ – 7:x² + 9x – 14, then find f(n) (x) for all r € N.

A: Using basic differentiation formula, find nth differentiation of  f(x).

Q: Let h(x) = f(x)g(x). If f(x) = 4x² – 3x and g(x) = In(3x – 1), what is h' (x)? Select the correct…

A: The given functions are fx=4x2-3x and gx=ln3x-1. Here,  hx=4x2-3xln3x-1.

Q: 6. Find y" of (1 – 2x)³

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 19) 1+ V3 mult. 2 A) f(x)= x* – 7x' + 8x + 4 B) f(x) = x* – 4x³ + 7x² + 8x + 4 - - 3 = x* + 4x' + 8x…

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Q: x+1 Find the slope of the tangent line to the graph of f (x)=; at a=0 2x + 1 A -1 B 1 C0 D None of…

A: fx=x+12x+1 Note:- As per the company's guidelines, we are supposed to solve the first question for…

Q: 3 • xy²-2y = x ²cos4x (x-2) • FY+ 2(x-2) ³

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.…

Q: Regula-Falsi Iterative Formula: Xnew = xp - [(f(xp) * (xp – xn)) / (f(xp) – f(xn))] Problem: f(x) =…

A: Solution:

Q: 1. If f(x) = ax² +b where a and bare real constants, then show that (a) f[xx] = a (x₁+x). (b)…

A:

Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: x-3 1. f(x) = x2 + 1 g(x)= v1–x h(x) = v(x) =-9 w (x) = 4x +3 r(x): %3D x+7 Find the following and…

A: Given that:                      f(x)=x2+1g(x)=1-xh(x)=5xv(x)=4x2-9w(x)=4x+3r(x)=x-3x+7   NOTE: As…

Q: 1 S (x) = - x - 4 Il discontinuous points of (see the graph) are

A: f(x)=1/x^2-4 f(x)=1/(x-2)(x+2) f(x) is defined when x-2≠0,  x≠2 x+2≠0,  x≠-2

Q: Find h(g(2)), where h(x) = In(1+x²) and g(x) = Ve2a – 1. - O 6 оз O 4 O 5 O Answer not listed O 2

A:

Q: If s(0)=−4, s(7)=−5, f(0)=2, and s′(x)=f′(x) on [0,7], determine the value of f(7)? (Do not include…

A: We have to determine the value of f7  given,  s0=-4, s7=-5, f0=2 and s'x=f'x on 0,7 Since, s'x=f'x…

Q: 3. Given the function y = -x² (1-2x)(-2x+3)(1-2×)² a) find the degree, leading coefficient, and the…

A: a) To find the degree, leading coefficient, and the value of the finite differences, we can start by…

Q: 20.) Find the linearization, L(x) ,of f(x)=x*+3x² values of f(x) when x=-1 , x=-1.1, x=-1.5 , and…

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Q: 3. h(x) = -2x³ + 5x² + 4x° – 3x + 12x? - 4 !! f (x) f(x) →_ as x → -00 as x → +00

A: We have to find the limit of the given function.

Q: 3 f(x) = x° – 9x s(x) 3 х?— 2х — 3 Which of the following expressions is equivalent to f(x) for x >…

A:

Q: 6. Let f(x) = 2x² + 4x + 1 and g(x) = 4x + 3 over Z5. Then f(x) g(x)= CF in Z5 [x].

A:

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

A:

Q: Q 6. If the function f(x) = 2x - 9ax + 12a*x+1 has a local maximum at x x1 and a local minimum at x=…

A:

Q: 4. Let f (g(x)) = (3x – 5)² + 1 and g(f(x)) = 3x² – 2. Find a single formula for f and a single…

A: We have given that f(g(x))=3x-52+1 and g(f(x))=3x2-2. We have to find for single formula for f and a…

Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: Find f(x) and g(x) such that h(x) = (f • g)(x) a. h(x) = V5x – 2 b. h(x) = 19x² – 4| c. h(x) = tan…

A: Authoring guidelines: As per the authoring guidelines we can solve only the first three parts of…

Q: Let f(x) = 2x – 3 and g(x) = 4x², then f(g(x)) = Select one: Оа. 3 — 8х2 оБ. 8х2 — 3 O c. 8x2 + 3 O…

A:

Q: If f(x) = 12sin(green wave), then the red wave isni %3D 20 |-31/2 |-T1/2 T/2 3h/2 2n 5T -10

A: Solution A sinusoidal wave can be represented as f(x)=Asin(2πfx+P)..........(1) Where A is amplitude…