Q3) if the continuous function is : 4x+1 F(x) -+k at x= h. Find the value of h,k.

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

Q: Find the values of a and b that make f continuous everywhere. x2 4 if x 3 a = b =

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Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - if x 3 a = b =

A: Given that,

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: 3. If f is continuous and | f(x) dx = 10, find af(x*) dr. Give proper reasoning.

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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: Find the values of a and b that make f continuous everywhere. x²-4 if x 3

A: If a function is continuous everywhere Then right hand limit and left hand limit on any point will…

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: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Let f(x) = V5x² – 20. Find everywhere f is continuous. -

A: Given fx=5x2-20

Q: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

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Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Determine the interval(s) for which f (x) = - 2x² is concave down. 12 %3D

A: For the curve y=f(x) to be concave downward,  f"(x) &lt; 0.

Q: What is the minimum number of times you would expect f(x) 6 in the interval (0, 40? %3D

A: from the given table we cansay (As f(x) in continuoun everywhere)∃ x1∈ (0,10) such that,…

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

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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: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

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Q: 10 if x c - everywhere then: С —

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Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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

A: Given f1=2f4=7f'1=5f'4=3 f''x is continuous To find value of ∫14xf''xdx

Q: Determine the interval(s) for which f(x) =- - 2x2 is concave down. 12

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Q: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

Q: Find the values of a and b that make f continuous everywhere. x² – - 4 if x < 2 X - 2 f(x) ax2 - bx…

A: Please refer the attached image for complete solution.

Q: f(x): 2x at x = 4 x2-3 f(x) = V3x - 10 at x = 2

A: According to question,a. Given function,fx = 2xx2 - 3

Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 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 a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

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Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

Q: Find the values of a and b that make f continuous everywhere ー if xcz 2-2 fac)= az²-bz +l, if 23 a =…

A: The objective is to find the values of a and b for which f(x) is continuous everywhere.

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

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Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: 2. Show by definition that the function f : R R, f(x) = ||, is continuous on R. Hint: you may need…

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Q: For what values of the constant c is the function f continuous on (-o, )? Show your work. S ex + 4,…

A: Please see the answer below

Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: Find the values of a and b that makef continuous everywh x2 – 4 - if x 3 a = b =

A: A function f is continuous when x=c is the same as saying that the function's two-side limit at x=c…

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: Find the absolute maxiom and minimum. for F f(x) = Xe 10the interual

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Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: Use the formal definition to show that the function f(x) = x³ + 4x2 is not uniformly continous on…

A: Consider the given function. fx=x3+4x2 Given a small positive real number ε, uniform continuity…

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: If f(2) = 13, f' is continuous, and | f'(t) dt = 27, f(6)? what is the value of Answer:

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Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

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