Let f be a differentiable function such that f(x + y) = f(x)+ f(y) +5xy and f(h) lim h→0 = 16. Find f'(2). h

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: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

A:

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

A:

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: If ƒ is a differentiable function, find the derivative Y = ƒ(√x) fı x + √√ f(x). 1 ○ y = ƒl (√√x) +…

A:

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

A:

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Use the graph of f and g. Let p(x) = f(x)g(x) and g(x) 2 (a) Find p'(4). p'(4) = = (b) Find q'(1).…

A:

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

A:

Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

A:

Q: Find the derivative of the function f(z) = 6z² – 18z by the definition of derivatives f'(z) = lim…

A: f(x)=6x2-18x

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: (20p) Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for…

A:

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

A:

Q: Consider the function f(x) = In (x - 4) a.) Use the First Derivative Test or the Second Derivative…

A:

Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

A:

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: 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: 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.