At what points are the functions in Exercises 13-30 continuous? 1 1 + 4 (x + 2)2 13. у 3x 14. y %3D x + 1 x² - 4x + 3 x + 3 15. у%3 16. у 3 - Зх — 10 | 1 Ir il + sinr

Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞0). fi(x)…

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Q: Let f(x, y) = 4æ? - 4x – 7y + 2y² + 10xy List the critical point: Preview

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Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

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Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(xi)…

A: Solution: (1) f''xi=fxi-2fxi-1+fxi-2∆x2 We know that f'x=fx-fx-∆x∆x and fxi-1=fx-∆x,  fxi-2=fx-2∆x…

Q: Compute the partial derivatives. f(x, у, 2) %3D 8x4 y7 + z6 af 3 32x 17 +-6 af – 56x ду _6 48x4 y'…

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Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: Find the partial derivative of z with respect to x (32) for z = (3x² + 1) cos(x²y) O None of the…

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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for…

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: 1.Test the function def ined by f(x.y)=xlnx- ylnx for its homogeneity. If it is homogeneous, give…

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Q: Determine the orthogonal trajectories of the family of electric field lines described by the family…

A: Given    x-c3+y2-c23x-c=x3   differentiate  w.r.t.x    3x-c2+2ydydx-3c2=3x2⇒2ydydx=3x2-3x-c2+3c2…

Q: xy ,show that: x- y If z = = 0

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Q: If f is a function of three variables that has continuous second-order partial derivatives, then…

A: This question  is based on a simple theorem

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: How many second partial derivatives does f(a,b,c, d) have?

A: Let p=fa,b,c,d. Note that, for a function of two variables p=fa,b there are four second partial…

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

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Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: Give the family of orthogonal trajectories of y^2=Cx^5+5.

A: To find →Family of orthogonal trajectories of y2=cx2+5 -1

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: x + y + 1 f(x, y) = , x ln (y² х — 1 -

A: A function f=f1, f2, ⋯, fn is said to be continuous at a if and only if the all the components f1,…

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: 6. let h be the function defines by h(x) = 2e***dt, Find h'(2) %3D

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

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: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

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Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

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: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Confirm that the mixed second-order partial derivatives of f are the same. f (x, y) = 5 In(x² + y²)…

A: Given:    f(x,y) = 5 ln ( x2 + y2 )

Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

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

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Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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Q: 4. Let F : R² → R² defined by F(x,y) = (2x +3y, –x +y). Is F a linear? Why?

A: Given

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

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Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

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Q: Suppose f has partial derivatives f,(x,y) = 3x-y and fAx,y) = 4y - x- 1. Classify each of the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: