3. Determine the largest interval where j(x) = Vr² – 1 is continuous.

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

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Q: Find a first degree approximation of f (x) = In x centered at x = 1.

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

Q: 8. If f is continuous and f(x) dx 10, find xf(x²) dr. %3D Give proper reasoning.

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Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

Q: Every continuous function on a, b\, that has absolute extrema on endpoints, must have one .(a, b)…

A: b. False Consider a continuous function f (x) on [a, b], that has absolute extrema on the endpoints.…

Q: What value of a makes ƒ(x) = x2 + (a/x) have a. a local minimum at x = 2? b. a point of inflection…

A: Given,

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: If functions ƒ(x) and g(x) are continuous for

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Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: Clarify that f f :(0,1) →R defined by f(x): not uniformly continuous. =-

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Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Evaluate f x2 dx using the limit defintion of the definite integral.

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

A:

Q: Determine the number at which h(x) = V16 – x² is continuous. %3D | Vx²-1 Determine the largest…

A: Note that: A function is said to be a continuous function on some interval when the function is…

Q: Find the lineari zation L (x) of the fuction at a. f) = x'+2x

A: In the given question we have to find linearization of function.

Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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Q: Determine the set of points at which the function F(x, y) = arctan ( 3x +7/y – 7 ) is continuous.

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Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

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Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

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Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Determine the largest interval over which the fu Vx+2 is continuous.

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Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: If c is a critical point of f(x), when is there no local maximum or minimum at c? Explain.

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Q: Find the interval(s) where f(x)= x²- 2x+3 is continuous.

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Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x < 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Find the global minimum of the function f (x) = 1+x² on the interval (-∞, 0) . Write DNE is there is…

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Q: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

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Q: j(x) = v2x – 4 %3D

A: We have  jx=2x-4   Function is continuous when 2x-4≥02x≥4x≥2

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

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Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)<0, then f(x) has local…

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: Find the local minimum xalue of f(x.y)= yds xy

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Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

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Q: 2. Suppose that f is a measurable function satisfying m{r ER: |f (x)| > n} ) < 1 nEN. n3 Is f…

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Q: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

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Q: Find the absolute maximum and minimum values of the f(x,y)= x²-2xy+y² function over the D region and…

A: In this question, we have given a function and the region D in figure the function f(x,y) and D are…

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

A: