Let (s n(x-y) |x|+ly\ = 0 f(x, y)={ |x|+|y]| (0, (x, y) = (0,0) Is f continuous at the origin? Why?

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: Iベ+g2 Let f(x y) s (x,y) = (0, 0) . ノ Is f Continuous at 10,0) ? why ?

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Q: Verify Eular's Theorem for the function xy+yz+zx

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Q: 12. Consider x²y f(x, y) = g4 + y? for (x, y) (0,0) and zero otherwise. Is f continuous at (x, y) =…

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Q: f(x) is a positive continuous function on R what does the function F(x)= | f(t) dt a represent (for…

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Q: iven F(x) = L- (1 – /1– (1+1)² ) dt valuate F(0) and F'(/2) using the First Fundamental Theorem of…

A: We have to find out

Q: De min Jx when f(x, y) = cos(y – x) – x sin(y – x). 1. fr = -x sin(y – x) | 2. fa = x sin(y – x) 3.…

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Q: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: The first order partial derivative of f(x, y)= x' with respect to 'x' is а. ух-1 yx- b. (у-1)x' c.…

A: For partial derivative with respect to x, we take y as a constant.

Q: Use differentials to estimate the change in f (x, y, z) = x² In(5yz + 1) as (x, y, z) changes from…

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Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

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Q: (2) Let f(x, y) = x² – y². Find the tangent line to the level curve f(x, y) = -3 at (1,2).

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Q: Find F '(x). F(x) 3 tan(t) dt %3D F '(x) = 0

A: Given that, F(x) = ∫0x3tan(t) dt We have to find F'(x).

Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

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Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: 3) To find the partial derivative of f (x. y) with respect to y at the point (xy. we A)…

A: Solving the question with an example

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Compute the partial derivative of the function f(x, y, z) = e'-z cos(y) +ze-/(1+y²) with respect to…

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Q: x²y- ry f(x, y) is continuous at (1, 1). x- y+1

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Q: The partial derivative of f(x, y) with respect to y at the point (x,y) is f(x+h,y)-f(x,y) h B f(x…

A: We have to Write the Partial derivative of f(x, y) with respect to y at the point (x0,y0).

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: 1 (x, y) = (1, –1) f(x, y) = x2 + Y (æ, y) + (1, –1) x + y is not continuous at (1, –1). [b]

A: Given :    f(x, y) = 1 ,(x, y) = (1, -1)x2+yx+y ,(x, y) ≠ (1, -1) To show :   f is not continuous at…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = ln t , z = e^(t-1) . F

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Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: Let f be a function with continuous first derivatives, defined by f (cos(xy), x2 + y³) xy If we take…

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Q: Show that following function xY (x, y) + (0, 0), f(x, y) = x² + y² (x, y) = (0,0) is continuous,…

A: To check the continuity of given function at origin firstly finding the limit of the function at…

Q: x-1, -1 sx< 0 0<x <1 x = 1 1<x< 2 2 <x<3 2r, f(x) = 1, -2r + 4, 0, Is f(x) is continuous at x = 1…

A: Given: f(x)=x2−1,−1≤x&lt;02x,0&lt;x&lt;11,x=1−2x+4,1&lt;x&lt;20,2&lt;x&lt;3 A function f(x) is…

Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: |(y) + (0,0) (x. y) (0,0) Show that the function f (x, y). is continuous at the origin however =…

A: consider the equation  f(x,y)=∑xyx2-y2x2+y2 ,0  x,y  #(0,0)xyx2+y2 where f(0,0)

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: 5.) Use linear approximation to estimate f(0.1, −0.9) x² sin x In(y² + 1) Y f(x, y) = of th + x+1…

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the approximate…

Q: Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at…

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Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

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Q: Find the linearization of f(x)=1−∫3x+124/(3+t)dt at x=2.   upper limit of integral = x+1 lower…

A: Linearization

Q: Find fy for f(x, y) = (In x) (sin x² y). O fy = (In x)(cos x²y)(2xy) O fy = (cos x2y)(x²) O fy = (In…

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Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

A: For this question of partial derivative we need to find out first derivative with respect to x and y…

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

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Q: (b) Determine whether (x, y) # (0,0) (r, y) = (0,0) f(x, y) = continuous or not.

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Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: w(x) = |x + 1| m at x = 1 Select the correct response: Continuous Continuous

A: For continuous function LHL is equal to RHL and function values same

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.