Let f be a differentiable function such that f(x + y) = f(x)+ f(y) +6xy and f(h) lim h→0 = 20. Find f'(2). h

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

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

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Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

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

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

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Q: Find a function

A: This is very intresting question because there are so many function on an interval whose first…

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…

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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. Given the following transformations on f(x)=√x, a vertical stretch of about the x-axis, a…

A: Given function We have to find the new transformed function

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: Let f be a function of x defined by ex f(x) + 15x-9x² =0. The derivative of f at x is f'(x) =

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

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Q: Consider the function y=g(x)=-x2+3. Use the limit definition of the derivative to compute a formula…

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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: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

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Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

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Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

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Q: a) Find dx of the function y = (x+1)²using the limit definition of the derivative. b) What is the…

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