Can someone help me solve this problem 19,21,23 4.1.2 Linear Dependence and Linear IndependenceIn Problems 15-22 determine whether the given functions are linearly inde-pendent or dependent on (-∞, ∞).15. f(x) = x,f(x) = x², f3(x) = 4x - 3x²16. f(x) = 0,f₂(x) = x, f(x) = e*17. f₁(x) = 5,f₂(x) = cos²x, f(x) = sin²xf3(x) = cos²x18. fi(x) = cos 2x, f(x) = 1,19. f(x) = x, f₂(x) = x - 1, f3(x) = x + 3f₂(x) = 2 + |x|20. f₁(x) = 2 + x,21. fi(x) = 1 + x,f₂(x) = x, f(x) = x²22. fi(x) = e*, f2(x) = è *, f(x) = sinh xIn Problems 23-28 show by computing the Wronskian that the given func-tions are linearly independent on the indicated interval.23. x¹/², x²; (0, ∞)24. 1 + x, x³;(-∞, ∞)

If Wronskian of f1,f2 and f3 is zero then f1,f2 and f3 are linearly dependent otherwise they are…

Answered: Can someone help me solve this problem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 x=-2 at a=-1 . Compare values of L(x) to 6.
Eх. (3) f(x) = xcosx, (0
Find the equation of the line tangent to the graph of the indicated composite function at the indicated value of the independent variable. 13) g(n) = 2n + 3 S(n) = n² + 2n² Find (g• f)(0) 15) g(x) = x + 5 S(x) = 4x – 5 Find g(s(-3)) 17) g(n) = n – 5 H(n) = n' + 3n Find g(H(0)) 19) h(a) = a + 1 Find h(H(-1))
6-Compute the following function values for D- F(2) and E- F(-2)
Q.5 Show that both of the functions f(x)=(x-1) and g(x)=x – 3x +3x-2 have stationary points at x = 1.What does the first and second derivative test tell about the nature of these stationary points?
4. Suppose the following functions are a general solution of: y(4) + a3y" +a2y" + a1y' + a0y = 0
14. Given the following graph of the function y= f(x), construct the graph of the function y= f"(x). (0,2), (1,3), (2,5), (3,9), (-1,1.5) -8 7- -5 -3 -9 -8 -7 -6 -5 -4 -3 -2 2 6 -2 Solution: https://youtu.be/plmnlQ2nb3g PRESS
Answer the following questions about the equation 1 4x³ − y² + −yz² − x(y − x)e² + 1 = 0. - (1) Does the equation define z as a function of x and y in a neighborhood of the point (xo, yo) (1, 1)? Why? (2) Does the equation define z as a function of x and y in a neighborhood of the point (xo, yo) (0, 1)? Why? (3) Does the equation define z as a function of x and y in a neighborhood of the point (xo, yo) (1, 2)? Why? = (4) In case (3), calculate the partial derivatives zã and zy at (xo, yo) and use them to approximate (in the spirit of the differential) the value z(1.1, 2.05).
3. Determine whether the function is even, odd or neither. (a) (b) g(x) = |r| + x² y = f(x); 4. Let f(r) = |x – 2|, g(x) = 3x +1 and the graph of h(x) is given. %3D y y=h(x) -5 Find (b) ) (-2) ()« (a) (f + g)(x) = (c) (goh)(3) = (d) (f o g)(x) = (e) (ho h)(2) =
Sp
11. What is (f+g) (y) for the functions f(y) = 5y²-2y+1 9(y)=-3y²-y-2. ○ (f+g)(y) = (f+g)(x) = 2y² +3y+1 ○ (f+g) (y) = (f+g)(x) = −8y² +y-3 ○ (f+9) (y) = (f+g)(x) = 2y² − 3y-1 O (f+g) (y) = (f+g)(x) = 8y²-y+3
1.7 If f(x) = 4x + 9 and g(x) = 3x – 1, find f(g(x)). a. 12х + 13 b. 12х + 8 С. 12х + 5 d. 12х + 26

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