Continuity of functions with several variables: Find and describe the points in the plane that the function f (x,y)=- X- y is continuous.

Q: Proof: Let f and g be differentiable functions such that f" #0 and g" # 0. Show that if f and g are…

A: Use the condition for a graph of a function to be concave up.

Q: |a| x2 – 1 Determine all points at which g(x) is differentiable. Justify your answer.

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Q: Linear Approximation 1. Find the linear approximation of the function g(x) = V1+x at x = 0 and use…

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Q: Analyzing critical points Find the critical points of the following functions.Use the Second…

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Q: Fundamental Theorem of Calculus Explainwhy the Fundamental Theorem of Calculus cannot beused to…

A: To determine why fundamental theorem cant be used to integratef(x)=1x-c on any interval containing…

Q: HAPTER 3 / STATIC OPTIMIZATION 4. Find the functions x* (r) and y*(r) such that x = x*(r) and y =…

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Q: The demand function for specialty steel products is given, where p is in dollars and q is the number…

A: Given information :  p = 105 100-q3

Q: Find the absolute extrema of the function on the closed interval. f(x) = 6 - x, [-4, 2] minimum (x,…

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Q: 不y y =x5 (0, у) (х, у) (0, 0) A right triangle has one vertex on the graph of y = x°, x>0, at (x,…

A: GivenA right tringle has one vertex on the graph of y=x5, x>0Another vertex is at the origin.and…

Q: Fundamental Theorem of Calculus.   Suppose that g(x) is a differentiable function on [a, b]. Express…

A: If we have F(x)=∫f(x)dx. Then fundamental theorem of calculus states F(b)-F(a)=∫abf(x)dx. The…

Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

A: A function f(x) is said to be continues at x=a, if LHLx=a=RHLx=a=f(a)

Q: Finding a Pattern Develop a general rule for the nthderivative of xf (x), where f is a…

A: Given derivative of xf (x), where f is a differentiable function of x. we need to find the pattern…

Q: Continuity At what points of ℝ2 are the following functions continuous? p(x, y) = ex - y

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Q: minimum and maximum values of the function f(x, y) = x² + y²

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Q: %3D Let H(x) = f(x) + g(x) and K(x) = f(x) – g(x). Use the graphs of y = f(x) and y = g(x) to find…

A: From the graph it can be said that,

Q: f(x) — х? + 7 — х, а %3D4

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Q: Functions Let the function f be differentiable on aninterval I containing c. If f has a maximum…

A: If a function f be differentiable on an interval I containing c, then it must be continuous on that…

Q: Differentiable Function. If a differentiable function f(x) satisfies f(-2) = f{2) then there exists…

A: Given that f-2=f2 we need to show that for what condition c∈-2,2

Q: Continuity At what points of ℝ2 are the following functions continuous?

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Q: Checking continuity Determine the points at which the following func- tion is continuous. 3xy? x? +…

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Q: ach of Exercises 19–24 gives a formula for a function y ach case, find ƒ¯'(x) and identify the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: - f(x) = |x² – 9| 12 10+ 2 -4 -2 2 4

A: we have f(x)=x2-9Now check the differentiability of the function.put x2-9=0⇒x2=9⇒x=±3

Q: Analyzing critical points Find the critical points of the following functions.Use the Second…

A: The given function is, fx,y=x2+y2-4x+5 Apply the procedure for Maxima-Minima, Solve for critical…

Q: Generalized Mean-Value Theorem: Let f and g be two functions, each having a derivative (finite or…

A: This is a problem of Cauchy MVT.

Q: Derivative rules Suppose u and v are differentiable functions att = 0 with u(0) = ⟨2, 7, 0⟩, u'(0) =…

A: Obtain cross product of u and v. ddtu×v=vu'+uv'ddtu×vt=0=v0u'0+u0v'0

Q: nential function f(x) = a* wh 21. y A (2, 9) -3 3.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Theoretical assignment Consider hyperbolic tangent function exp(x) – exp(-æ) exp(x)+ exp(-æ) tanh(x)…

A: Linear Spline Intepolation: A linear spline is a sequence of straight lines. So, in between the data…

Q: Slope of a line Consider the line ƒ(x) = mx + b, where m and bare constants. Show that ƒ′(x) = m for…

A: Consider the following function: fx=mx+b Differentiate fx with respect to x:…

Q: Continuity: Iff and g are both functions that are continuous at some point a then

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Q: Continuity At what points of ℝ2 are the following functions continuous? g(x, y) = ln (x - y)

A: Given function: gx,y=lnx-y Here the  function is the composition fpx,y Where, the value of…

Q: Continuity. Find out, and give reason, whether f(z) is continuous at z = 0 if f(0) = 0 and for z #0…

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Q: Continuity At what points of ℝ2 are the following functions continuous? ƒ(x, y) = x2 + 2xy - y3

A: Given ƒ(x, y) = x2 + 2xy - y3

Q: Using Cauchy-Riemann equations, show that the function f(z)=(z+6)^2 is differentiable everywhere

A: The given function is       f(z)=z+62⇒f(z)=z2+12z+36                   -(1) Substitute the value…

Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Convolution. Find the convolution of (a) Πα * Πα. (b) f(x) * ƒ(x), where ƒ(x) = e¯\ª\, -∞< ï<∞.

A: As per the question we are given two functions as: Πa(x) : the rectangular pulse function with…

Q: Clairaut's Theorem Give one example of a function where the Clairaut Theorem fails, and justify your…

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Q: Let X bearandomvariable and let g(x) be a no0negative function. Then for r>0,0, P [g(X) ≥ r] ≤…

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Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

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Q: Analyzing critical points Find the critical points of the following functions.Use the Second…

A: The function given is ƒ(x, y) = x4+ y4 -4x -32y +10. Take the first derivative of the function,…

Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

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Q: Limits of functions of three variables Evaluate the following limits.

A: We have to find limits of the functions: limx, y, z→1, -1, 1xz+5x+yz+5yx+y As it is 00 indeterminate…

Q: Average Price of Land The rectangular region R shown in the accompanying figure represents a city's…

A: answer = $174.92   explanation is given in below step

Q: X- a, =} 4, (bx +1, X -3

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Q: (Quotient Rule). Let I be an interval and let f,g:I → R be differentiable at cE I. THEOREM Then…

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Q: Continuity of functions with several variables: is X-Y 1. Find and describe the points in the plane…

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Q: diiferential of a function: f(x,y)=ye^x at (0,-2)

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Q: Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by p = f(x) =…

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Q: Use a graphing utility to graph the function and find the absolute extrema of the function on the…

A: solve the following

Q: Show that f'(z) does not exists any point z when f(z)= Im z

A: We have to show f'(z) does not exists at any point of z where f(z)=Imz