x < 3 3 sxs 4 x > 4 kx + 3, а. Let g(x) = 8, a) Find the value of k if g (x) is continuous at x 3. b) Determine whether g (x) is continuous at x = 4. + 1 x < 0 b. Given f(x) = 0

Q: If possible, choose k so that the following function is continuous on any interval: 7z³-21z¹ z-3 x =…

A:

Q: Let f(x) be a continuous function on (-00,0) and f"(x) = (-4x + 5)e4x. The function f(x) has an…

A:

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

A:

Q: Find the particular solution of the initial value problem. 4y" – 4y' – 3y = 0, y(0) = 1 and y'(0) =…

A:

Q: Determine if the function is continuous at the indicated point 12 1 f(z) = |2|= 1

A: To determine if the function f(z) is continuous at ∣z∣=1, we need to check the following: The value…

Q: 4) (1, 4) 2) (3.-4) (-4, 5) Determine if f is continuous at x = c. (a) x = 4 (b) x = 1 (c) x = -1…

A: Given   The graph of the function  Definition of Continuity :-  A function f is continues at x= c…

Q: V2(x+3): xEQ x² + 3x: x €Q Let f: R R be defined as f(x)=. The set of all points at which f is…

A:

Q: . Let G(x)= x+3)2, if x ≤ -1; 2-x if 1<<1; Find all values of a where G is not continuous. , if x 1.

A:

Q: (a) Given Ax-6, x6. (i) Calculate the value of A. (4 marks) (ii) Examine whether the function is…

A: Continuity

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

A:

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

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

A:

Q: Find and classify the extreme values of f(r)=6r 4r over the interval (-2 21

A:

Q: (4ах + 2b , X<1 2х — 3Ь,1 <х < 3 (2ах + 4b g(x) ,3 <x Find the values of "a" & “b" if gm is…

A: We will find the value of a and b as following-

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

A:

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

A:

Q: 6) Determine constants a and b such that f(x) is continuous for all values of x. ax + 3, if x> 5 8,…

A:

Q: (x2+3). Explain why √x4+24 Q7. Consider the function f : [0, 1] → R, x→ (a) f continuous, (b) f is…

A:

Q: 1. From the graph, determine the function f (x) is continuous at x = -1. f(x) 3 %3D %3D -5 -4 -3 1…

A:

Q: Find all values for which h(x) = (x + 2)(x − 3) (x + 2)(x − 1) fails to be continuous. Explain your…

A:

Q: x2+2x+5. Show, x+2 Q1 Let f: R\ {-2} → R be given by f(x) directly from the definition, that f is…

A:

Q: Decide if f(x) is uniformly continuous on the interval. Explain

A:

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

A:

Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

Q: Suppose that f(x) is a continuous function on the interval [0, 4] with f(0) = -10 and f(4) = 10.…

A:

Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

Q: Find a and b so that f(x) is continuous if f (x) = Ⓒa = ²/1 b = 60 96 a = - ²/2 b = 29/4/20 -²/26 =…

A: