Create a linear function over [2,4] that has an area of zero.

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Determine whether the given set of functions is linearly independent on the interval (-∞, f_ (x) =…

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Q: Show that F = ху, , zy) is not conservative. 2

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Q: ded on the y-axi

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a…

Q: Tell whether the enumerated function is linearly dependent or linearly independent using wronskian.

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Q: Show that the functions f, (x) = 4x" , and f2(x) = x"** are linearly independent on (-00, 00).

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Q: Show that the limit of the function f(x,y)= (0,0). (x+y)² x² + y² is indeterminate at

A: Limit of the function

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f" is continuous. Find the value of *…

A: Use the method for integration by parts to solve the integral.

Q: Find the linearization at x = a. f(x) = 6x®, a = 1

A: Linearization L(x) of function f(x) at a is given as L(x) = f(a) + f'(a)(x-a)

Q: Determine the are bounded by: y2-8y+8x=0, and x=0

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Q: show that the scalar t that minimizes ||y– tx||

A: In this question, we need to find the t that minimizes ||y-tx||.

Q: The inner-product function satisfies : Select one: a. = b. = 0 C. is greater then zero d. =

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Q: Define a weakly quasi-concave on a Cobb-Douglas Function

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Q: Show that the functionf (x ,y)=xy³onD: x|<2, ]y|<oodoes not satisfies Lipschitz condition.

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: Define f(x) so that the average value is 10 on 0 < x < 6 where f(x) is a polynomial function that is…

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Q: Verify Cauchy's MVT for f(x) and f'(x) in [4,9] where f(x) = Vx %3D

A: Cauchy's MVT : If two functions f(x) and g(x) are continues on [a, b] and differentiable on (a, b),…

Q: Let f(x, y) = xy - 4x on

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Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

Q: Show that the function f defined by (r, y) = (1, –1) (r, y) # (1, –1) f(r, y) = 1² + y is not…

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Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: Define Wronskian of Linearly Dependent Functions?

A: We have to define the Wronskian of linearly dependent functions: Let f1 ,f2 ,...,fn be n real or…

Q: 7. Determine whether (u,v) =3u, v, – 2u, v, is a valid inner-product function or not for R²

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Q: Show that exp(x), x exp(x), and x? exp(x) are linearly independent functions.

A: TO FIND: Show that exp(x), x exp(x), and x2 exp(x) are linearly independent functions.

Q: Suppose that u(x) is a differentiable function such that

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Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x) F(x) |Vt4 + 1 dt -7

A: 2nd Fundamental Theorem : For F(x)=∫axf(t) dt, if f is continues on [a, x], then F'(x)=f(x).

Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: Every continuous function on a, b, that has absolute extrema on endpoints, must have one critical…

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Q: State the properties of the Bassel function.

A: Here we to state the properties of the Bassels Function.

Q: Use linear approximation to estimate f(3.85) given that f(4) = 5 and f'(4)= 6.

A: Given: - The values, f(4)=5 and f'(4)=6 To estimate: - The value of f(3.85) by using linear…

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

A: Given fx=x+1x

Q: Determine the are bounded by: y2-8y+8x=0; and x=0

A: The polynomial y2-8y+8x=0 can be rewritten as x=8y-y28. The function is graphed to understand the…

Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: 8(x) = X -x3 + 2x x4

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Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

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Q: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of…

A: To Determine: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the…

Q: Suppose div(F(5,3,2)) = 240. Estimate the flux of F out of a small, outward-oriented box of side…

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Q: What are Continuous Variables?

A: Continuous variables are numeric variables that have an infinite number of values between any two…

Q: {x+ 2x³,3+x, 1– x} on the interval [–1,1]

A: The given set of functions are: x+2x3,3+x,1-x and the interval is -1,1

Q: Suppose that f (1) = 2, ƒ (4) = 7, f' (1) = 5, f' (4) = 3, and f" is continuous. Find the value of…

A: Given data: f(1)=2 f(2)=4 f'(1)=5 f'(4)=3 The objective is to find the value of ∫14xf''(x)dx Apply…

Q: The inner-product function satisfies : Select one: O a. = O b. = O c. = 0 O d. is greater…

A: We will use the definition of inner product function.

Q: 2. Show that the function. 5x²³²Bin 12 F(x)= โ x2 0 (x=0) is not of bounded variation on [1,1].…

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