If x is a r.v. with c.d.f. F(x), F(x) is continuous at x = 10, then P(X= 10) = 0. True False

Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: Suppose ƒ is continuous on [1, 5] and 2 ≤ƒ(x) ≤ 3, for all x in[1, 5]. Find lower and upper bounds…

A: If f:[a,b]-->R is a continuous function then f is integrable over [a,b].

Q: 4 For what value(s) of x is the function f(x) 2x? - 6х NOT continuous? A. x = 0 and x = 3 B. x = 3…

A: To find- For what value(s) of x is the function fx = 42x2 - 6x NOT continuous? x = 0 and x = 3 x =…

Q: Let f(x) be a continuous function. If f(c) is an absolute max or absolute min, then c is unique. O…

A: Given,  fx is a continuous function fc is absolute max or absolute min , then c is unique.  We have…

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

A:

Q: If f is continuous, then b+c f(x)dx = ] -S Fx - c)dx f(x – a+c

A: Translation along the horizontal axis can be obtained using the transformation rule x→x-a on the…

Q: If f is a function that is continuous on the open interval (1, 4), then f is continuous at x = 3.…

A: Given: If f is a function that is continuous on the open interval (1,4), then f is continuous at…

Q: Suppose f is a continuous function with x = a in its domain. Part 2 of the Fundamental Theorem of…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

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

A:

Q: If a function f(x) is not defined at x-z, then it is not continuous at interval (a, b) where a > z <…

A: Solution

Q: On which of the following intervals is f(x) = x x-7 concave down? (-00, 3) A. (4, 5) O B. В. (5,6) O…

A: Given:

Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

A:

Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

A:

Q: Find the values of c and d that make the function 6x if x 2 continuous. с — d =

A:

Q: Determine whether -2, if z < -2 *, if - 22122 |8- z), if 2<z <3 |4 -r, if z 23 f(a) = is continuous…

A: givenf(a)=-2, ifx&lt;-2x5 , if-2≤x≤28-x , if2&lt;x&lt;34-x2 , ifx≥3one limit of this piecewise…

Q: Determine whether the following functions are continuous at x = 2: 17x + 3 13x +7 x<2 f(x) = x22

A: In calculus, a function is continuous at x=a if and only if all three of the following conditions…