1. The smooth function f: R → R satisfies f(0) = 0, f'(0) = 1, f"(0) = 0, f(1) =1, f'(1) = 3, ƒ"(1) = 14. Construct a polynomial p(x) = Σio ax that interpolates f at all given values by using divided differences.

Q: Choose the gradient of the function \(f\) defined by f(x y) √1 (4x 5y)². O None of the others 4x+5y…

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Q: Let f and g be functions such that f(0) = 3, g(0) = 5, f' (0) = 4, g'(0) = -3. Find h'(0) for the…

A: Given f0=3,    g0=5f'0=4,   g'0=-3hx=gxfx To find h'0

Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: h" (t) = sec? t – Vt, h(0) = -3, and h'(0) = 3. %3D

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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: Find the weak derivative of f(x) = |x² − x + 1/5 on the - 1) interval (0,1).

A: 1.Given: fx=x2-x+15.To Find: The weak derivative of the given function on the interval 0, 1. Note-…

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: 9. Find a function f such that ƒ'(x) = x5 + 20 and the line 12x + y = −20 is tangent to the graph of…

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Q: 9) Sketch the graph of a function f(x) on the interval (-4,4) with the following properties. f(x) is…

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

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Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: Suppose you know that the function f is decreasing and concave down on t interval [2, 7]. which of…

A: If the first derivative of a function is negative then the function is decreasing and vice versa.…

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

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Q: 1. Let f(x)=√x-2 / x-4 . Show that f(x) has a removablediscotuiti t x=4   2. Given f(x)= √(x+1).…

A: Here we have to find the derivative of a function at a point.

Q: A particle moves along the x-axis with position function a (t) = 4 sin for 0 <t< 4n where t is…

A:

Q: f(x) = 2/1/2 and g(x)=3x+1, find the following: b) (gof)(x) 8. Let f(x)= a) (fog)(x) c) (fof)(x) d)…

A: according to bartleby guide line we do only first part of multiple questions given  f(x)=1x2  and…

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: 3. Use the graph of f '(x) to sketch the graph of f(x). Sketch f(x) on the coordinate plane below…

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Q: et f(x,y)= x^2-xy+y^2-y   what are the min and max values of Du f(1,-1)?

A: Given :  f(x,y) = x2-xy+y²-y  To find :  Maximum and minimum values of directional derivative at…

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then,…

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

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Q: 1. Determine whether the given functions are differentiable (anywhere). If the function is…

A: We will check where given function is differentiable and then we will find the derivative of…

Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

A: a)Given , gx=fx,yx Then, g'x=∂f∂x+∂f∂yddxyx  [∵y=yx]⇒g'x=∂f∂x+∂f∂yy'x

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: Consider the table of vales for the functions r). J ), u() and g'(x): If the function k is defined…

A: Given, k(x) = f(g(x))