5. Find interval where the following functions is continuous. a). f(x) = Vr +1 b). f(t) = r+3 47-1

Q: For what value of b is             continuous at every x?

A: To find the value of a such that given function is continuous for every x. f(x)=a2x-2a,    x≥212,…

Q: Suppose that f( is a continuous function. If f(#) da=4, then what is the value of T - f(x)] dæ ?…

A: To evaluate the given definite integral.

Q: Suppose that a continuous function g satisfies: 3 g(x)dx = 6 and | 9(27)dz = 9. 0, | z9(3z*)dz. Find…

A:

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: 4. Integrate the following function using the Trapezoid Rule with n=5: (1.2

A: As indicated in the question, we will make use of composite Trapezoidal rule to approximate the…

Q: 3. Use the definition to show that the function f(x) = is continuous on the interval [c, o0), where…

A:

Q: Based on your work in part a, on what interval(s) is f(x) continuous?

A:

Q: Determine the values of x at which the function in Figure 18 is: (a) dis- continuous and (b)…

A: (a) Here from the graph, we can see that, The graph has a break at the point x =1, that is, Thus…

Q: Suppose f is differentiable on some open interval containing e and f" (c) = 0 then (c, f(c)) is a…

A:

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

A:

Q: 6. Suppose that ƒ is differentiable on (a,b). interval [a, b]? Justify your response for find a…

A:

Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

A:

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

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

A:

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

A:

Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

A:

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) >0. Does f have a local…

A:

Q: For what interval is f (x) = xe concave down?

A:

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

A:

Q: Suppose that f is continuous and that f(z)dz = 0 and f(z)dz = 7. Find | 5f(x)dx. %3D - - 2 - 2 2 ОА.…

A: Given, ∫-25f(z)dz=7 To find -∫255f(x)dx

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

A:

Q: If f:R to {0,1} and I is an interval on which f has both values , the f has a discontinuity in I.…

A: Given that f has both 0 and 1 in its range.  This means there will be some x and y values for which…

Q: If f(3) = 15, f' is continuous, and I f'(t) dt = 24, what is the value of f(4)? %3D

A: In this question, f is a primitive function and we have to find f(4). So I am providing the…

Q: , find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

A: From the given problem: 57).   fx=12x+1,x≤23-x,x&gt;2   As we know that, if L.H.L is not equal to…

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

A:

Q: Consider the following. S-3x, f(x)={2 - 2x+ 9, x > 2 Find the x-value at which f is not continuous.…

A: We will find the value of x at which the f is not continuous and whether the discontinuity is…

Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

A:

Q: 14. Consider the following function: if - 10 SIS0 3. h(r) = {15x - 3| if 0<<4 2r +1 if r24 What is…

A:

Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

A:

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

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

A:

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

A:

Q: If X is continuous on the interval 0 to 10, t O True False

A: For a continuous distribution, and there exist infinite points.

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

A:

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

A:

Q: 4) Is the following functions continuous? for x < 1, d(x)= x- 2 for 1 < x.

A:

Q: On what interval is the function f(x) = x^3 - 4x^2 + 5x concave upward?

A: Use given function find the required result

Q: Find the values of the constants a and b, that make (ах + b, ifx3 Both continuous and differentiable…

A:

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

A:

Q: j(x) = v2x – 4 %3D

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

Q: If f(1) = 13, f' is continuous, and f'(t) dt = 28, what is the value of f(4)?

A:

Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

A:

Q: Graph the function and observe where it is discontinuous. f(x, y) = e1/(x - y) fis discontinuous at…

A:

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

A: