If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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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: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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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: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 x - 2 ax2 - bx + 3 if x < 2…

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: -x²+5 < f (x) < x+1 2

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Q: Find the values of a and b that make f continuous everywhere. 2-4 x 2 if x < 2 f(x) if 2 s x< 3 if x…

A: To determine the values of a and b so that f(x) is continuous everywhere.

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: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

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

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

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Q: f continuous everywhere. f(x) =   x2-4/x-2      if x < 2

A: Given fx=x2-4x-1if x&lt;2ax2-bx+3if 2≤x&lt;32x-a+bif x≥3 fx is continuous everywhere. Aim: Find…

Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: limit as x----0 for the function (px)/(sqrt(bx+a^2))-a using L'Hopitals

A: Apply the limit.

Q: find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable?

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

Q: Evaluate the limitlimx→0+x sin(x) + x^2/ x^2

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Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Show that the function is continuous on  (∞ , -∞).

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 ax2 - bx + 1 4x…

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Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: for x 1 x -1 = ( JI- 2 for x = 1, show that flx) is continuous at x = 1

A: If fx=x2-1x-1  for x≠12  for x=1then to show that fx is continuous at x=1.

Q: Show that x + is increasing on [1, 0).

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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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: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Suppose f" is continuous on (-o, 0). (a) If f'(2) = 0 and f"(2) = -2, what can you say about f? (b)…

A: Application of derivative problem

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

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: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

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Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: is: The interval of continuity of flx) = /2x – 10 OA[5, +0) OB.(-5, 51 OC(-0, + x) OD(-00,-5)

A: Function f(x) is continuous on interval [a,b] if it is continuous at every point.

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

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Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.