Hence use your polynonial to approximate f'(x),J"(x), J"(x), J'(1):f"(1),"(1). (d) Using Lagrange's formula, find a polynomial which passes through the points (0, – 12), (1,0), (3,6), (4, 12)

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: For the function f(x)=simplify the difference quotient: b) [(x+h)-700 What is the slope of the…

A:

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Let f(x) = √6-x The slope of the tangent line to the graph of f(x) at the point (2, 2) is The…

A:

Q: Find y as a function of t if 5184y" – 1584y + 121y = 0, - y(0) = 6, y'(0) = 3. y =

A: We have to find the general solution of the given problem.

Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Consider the function - f(x, y) = 2x² + xy² − 6xy + 5x +2. (a) Show that (1,3) is a stationary point…

A:

Q: What is the slope of the line tangent to the curve √√x + √y = 2 at the point 1 3 (A) -3 (B) (C) 1…

A:

Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: If f(z) is analytic function and u(x,y) = x3 - 3xy find f(z) %3D

A: Given that the real part of the analytic function f(z) is, u(x,y) =x3-3xy To find the analytic…

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

Q: For f(x) = x? – 2x – 1, find f(2), f'(2), and f(3) – f(2). - a. f(2) = -1 b. f'(2) = c. f(3) – f(2)

A:

Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

Q: Find y as a function of a if y" - 3y" y + 3y = 0, y(0) = -7, y' (0) = -4, y" (0) = 9. y(x) =

A:

Q: ) Use L(x) to approximate f(16.1).

A: For a given function f(x) the linearization at a point x=a is denoted by L(x) and it is defined as…

Q: te r'"(t) and r'(t) for the fo

A: Given that : The function is r(t) =t+4 i + tt +7 j - e-t2 k .