Scx? + bx, 3 — х, x > 1 f (x) = X < 1

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: If g(s,t) = f(s^2 - t^2, t^2 - s^2) and f is differentiable, show that t(∂g/∂s) + s(∂g/∂t) = 0

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: NOTE: Refresh your page if you can't see any equations. . here we have the given function is

Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)&lt;0. then function strictly…

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Suppose u and y are functions of x that are differentiable atx = 0 and that u(0) = 5, u(0) = -3,…

A: To Determine: find the values of the following derivatives at x=0                a)ddx(uv), b) ddxuv…

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Find the general antiderivative of f(x) = 4x – 5. Use Cfor the arbitrary constant. nswer F(x) =

A: Fx=∫fxdx

Q: . Find all values of the constants m and b for which the function S sinx, y mx + b, x 2T is a.…

A: To find all values of m and b for which the function:   y=f(x)  =  sinx    x&lt;π…

Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: Find ∂z/∂x for1/x+1/y+1/z= 1. Assume that the equation implicitly defines z as a differentiable…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: we have to find

Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

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Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

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Q: Which of the following is NOT differentiable at x=4? f(2) =+4 x - 4 ... A x + 4 ... f(x) = (x – 4)²…

A: If a function f(x) is differentiable at x=k then f'(k) must exist in the domain. If x=k is not in…

Q: Suppose that y is a differentiable function of x and z = cos (x5y6). dz in terms of x, y, and dY dx…

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Q: If the equation x²e+z_224cos(x-224z)=n?e+224 defines z implicitly as a differentiable function of x…

A: Since you have asked multiple questions, we will solve the first question for you. The other…

Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

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Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given y=3x2-5x a. We need to find the value of dy/dt when x=2,dx/dt=3. the value of dy/dt=21 when x…

Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: 17 If f(x)dx =17 and F(5) = 3, ( where F is an antiderivative of f(x)), what is the value of F(2)?

A: First we integrate using the fundamental theorem of calculus

Q: The graph of a differentiable function f on the ir [2,10] is shown. Find the trapezoidal approximat…

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: dz Suppose z is a function of r and y, and csc Vr2 + yz = zesin z. Solve for dz and dy

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Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: If the derivative of the closed function x2 + 2x – 3y + y² +m = 0 at the point (1, 1) is available,…

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Q: Let x and y be differentiable functions of t, and let s = /4x + 6y be a function of x and y. Answer…

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Q: If the equation x?ev+z_184cos(x-184z)=²e+184 defines z implicitly as a differentiable function of x…

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Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

Q: Find an antiderivative of f(x) 28. Assume that the value of the arbitrary constant is 0. Answer

A: Antiderivative of function

Q: Find all values of the constants m and b for which the function S sin x, y : тx + b, х 2п is a.…

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Q: Suppose that the functions f and g, with linear approximations L, and Lz at x = a as shown below.…

A: Limit problem

Q: if (2,y) # (0,0) Let f(x, y) = aª + yª Show that D1f(0,0) and if (2,y) = (0,0) D2f(0,0) exist but f…

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Q: if z=0 ne function f(z)= )² if z+0 is differentiable at z= 0 LL

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Q: 36 – t2 dt. f(x) 4+ cos? (t)

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Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:…

A: prove of the above question is given below...

Q: Suppose u and v are functions of x that are differentiable at x= 0 and that u(0) = - 4, u'(0) = 4,…

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Q: Please solve the Vƒ of the function below at point P. a) f = (x² + y² + 2)-05, P; (12,0, 16) b) f =…

A: a) The given function is f=x2+y2+z2-0.5. This gives ∂f∂x=-0.5 x2+y2+z2-0.5-1…