B- If f(x) = is continuous at x = Find A? |Ax2 x2

Q: f is continuous iff f-1(E) is closed

A:

Q: Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

A:

Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

A:

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

A: Given fx= x2-4x-2 if x&lt;2ax2-bx+1   if 2≤x&lt;34x-a+b      if x≥3Here f is continuous everywhere…

Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

Q: Find the constant a such that the function is continuous on the entire real line. (x) = {4x?, ах —…

A: We have to find a

Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

A:

Q: Suppose that f is a function on the interval [1, 3] such that –1 < f(x) < 1 for all x and f(x) dx…

A: It is given that ∫13fxdx=0 and -1≤fx≤1.

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: Consider the function f(x) : Find the value of B such that (3x + B if x> 3* f(x) is continuous at x…

A: Given: fx=2x2+3  if x≤33x+B   if x&gt;3

Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

A:

Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

A:

Q: h(x) = { 3-2 -2 if x≤-1 Cx² + 4x if x>-1

A:

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

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

A:

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

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

A:

Q: 45. For what value of the constant c is the function f continuous on (-∞, ∞)? Scx? + 2x if x 2

A: Let f(x)=cx2+2xif x&lt;2x3-cxif x≥2

Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

A:

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

A:

Q: Suppose that f(x) = SBx? – 3 if if (Bx+2 x> 2 Find the value of B so that f(x) is continuous…

A:

Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

A:

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

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

Q: For what values of a and b is -2, - b, -1 < x < 1 3, f(x) = ах continuous at every x?

A:

Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

A:

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: 86. If f is continuous and f (x) dx = 4, finc

A: Given that: ∫09f(x)dx=4

Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

A:

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

A:

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

A:

Q: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: 2 2 If f is continuous on [0, 2] and / f(x) dx = 5, find the value of | f(x – 2) dæ.

A:

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

A:

Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

A:

Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

A:

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

A:

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

A:

Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

A:

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.