3. For what value of b, f(x) is continuous at every x? f(x) = {, x < -2 bx? x > -2

Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

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

A:

Q: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: Given function

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

A:

Q: If f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) 3, and f"(x) is continuous, what is x f"(x) dx? %3D

A: Given: f(1)=2f(4)=7f'(1)=5f'(4)=3I=∫14xf''(x)dx=?

Q: For what value of b is

A: The given function is continuous for all x&lt;0 and for all x&gt;0, because it is a polynomial…

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

A:

Q: For what value of b is X - b b + l' x 0 continuous at every x?

A: The given function is gx=x-bb+1if x&lt;0x2+b if x&gt;0. If the above function is continuous at x=0,…

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

A: We need to show f takes value 4.

Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

A:

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

A:

Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

A:

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: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

A:

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

A:

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

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

A:

Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

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

A:

Q: For what value of the constant c is the function f continuous on the interval (-0,00). f(x)={ cx+1 ,…

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: 3. For what value of a, f(x) is continuous at every x? Sx2 – 1 2ax x 3 f(x) =

A:

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

A:

Q: 25 If f is continuous and f(x) dx = 12, find xf(x?) dx.

A:

Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

A:

Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

A:

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

A:

Q: Find the value of the constant c such that the function f(x)= (x-2)/( (root 4x+1)-3) if x#2, c if…

A: And

Q: For what values of a and b is Continuous at every x? -2, x 1

A:

Q: Consider g(x) = rº/3. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: We find g'(x) using the power rule  Then we find the left and right-hand limits of g'(x) and g'(0)…

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

A:

Q: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

A:

Q: x²-1 for x# 1 - If flx) = show that flxx) is continuous at x = 1 x-1 2 for x = 1,

A: topic - limits and continuity

Q: Is the following statement correct? If the function f is continuous at x=1, then the constant a…

A:

Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

A:

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: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A:

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for x 2…

A:

Q: For what value of a is the function continuous at every x?

A:

Q: 22 + a For what value or values of k is f(x) = ka + 3k - 5 continuous at a = 5?

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point, take…

Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.

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.