Show whether the following function is continuously differentiable: f(x,y)=x3 +y3

Q: Let f (x), g(x) be two continuously differentiable functions satisfying the relationships f'(x) =…

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Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: Let f and g be differentiable functions such that f'(0) = 3 and g' (0) = 7. If h(x) = 3f(x) - 2g(x)…

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Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

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Q: Find f. f"(x) = cos(x), f(0) = 6, f'(0) = 4, f"(0) = 9 f(x) =

A: We can find the value of f(x) as below.

Q: 1. Assume f(r) is a twice continuously differentiable function on the closed interval (a, b), which…

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Q: Find a function f and a real number a such that 4 + | f(t) dt = x tan -1 x. -

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Q: Let f(x, y) = ln(x + y − 1). The domain of f is {(x, y)| x + y > }.

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Q: find f. f '''(x) = cos(x),    f(0) = 2,    f '(0) = 5,    f ''(0) = 8 f(x)=

A: Given function and values are

Q: 6. f(x) dx = 2, find If f is continuous and xf(x2) dx.

A: given f is continuous and ∫09 f( n) dx = 2 we have to find ∫03 xf (x3) dx = ? we solve this by the…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, oo).…

A: Given,           Let f(x) be a function that is defined and has a continuous derivative on the…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. f…

A: Given, fx=xx2+16

Q: 2. Let f : R → R be a differentiable function. Show that the function f', the derivative function of…

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Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x<1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: Let f (æ) be a twice differentiable function such that f (0) 4, f(3) 5 and f' (3) = 6. Find the…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x" sin x %3D n = 1 f'(x) = n =…

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: Determine whether a given function is homogenous or not homogenous: 1. f(x,y) = sin x 2. f(x,y) = x…

A: Since there is a mistake in third question i do first two question as per our company guidelines…

Q: Consider the function f(x) = 5x + 9. Its tangent line at x = 3 goes through the points (7, yı) and…

A: Find the equation of tangent using derivative then satisfy the given points.

Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

A: Given that, f(x)=15x-5sin3x2x3, x≠0c,                          x =0 The function is continuous when…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x sin x n = 1 f'(x) n = 2…

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Q: find a non zero value for the constant k that makes the function fx={tan k(x) /x ,x0}continuous at…

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Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

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Q: A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 13, f(1) =…

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Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: Determine whether z is a function of x and y. z + x ln y − 8yz = 0

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Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: Find a and b such that f is differentiable everywhere.

A: The given piecewise function is: fx=ax3,      x≤2x2+b,   x&gt;2 This function is differentiable…

Q: Consider the function f(x) = 3cos(2x). (a) Find the derivative of f(x). (b) Verify that the…

A: (a) Given function is f(x)=3cos(2x) The derivative, f'(x)=-6sin(2x)

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x² sin x n = 1 n = 2 n = 3 n =…

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Q: f is a function of only x, g is a function of only y, and f and g satisfy ln(f(x)) + ln(g(y)) = ln(1…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x" sin x n = 1 f'(x) n = 2…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: Find the derivative of the function f for n = 1, 2, 3, and 4. %3D f(x) cos X %3D n = 1 f '(x) = n =…

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Q: Consider the function f(x) = 9x² +3. Its tangent line at x = 6 goes through the points (1, y1) and…

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Q: Consider the function f defined by f(x)=(e^x)(sinx) with domain [0,2pi]. Find the absolute maximum…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: Let f(x), g(x) be two continuously differentiable functions satisfying the relationships f'(x) =…

A: Introduction :

Q: f(x,y) = x [(In x)2 + y2] %3D find the extreme points of the function

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Q: Find f. f"(x) = cos(x), f(0) = 2, f'(0) = 8, f"(0) = 5 f(x) =

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Q: Find the function f(x,y,z) with a magnitude y.

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 13, f(1) =…

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x 3 a 3D

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Q: Find a value of the constant k, if possible, that will make the function continuous everywhere.…

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