Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z = 0

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

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Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

Q: Find and classify all stationary points of the function f(x,y) = x³ + xy + y² − x.

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: "; Find y as a function of x if x?y" + 5æy' – 21y = x°, y(1) = 7, y(1) = -5. y =

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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: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

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Q: Let f (x, y) = Vy – 2x Evaluate f(3, 10)

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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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: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Determine the expression for Fyz(x, y, z) given the function F(x, y, z) = 2x²y – xz? 3y z.

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Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: f(x,y) = x=y - 2xy? + 3xy +4 %3D

A: Given function is fX,Y=X2Y−2XY2+3XY+4 We have to find the global maximum and minimum of this…

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: 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: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: Show that the given function is not analytic at any point but is differentiable along the indicated…

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Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,