1. Study the continuity of f (x) at x = 2 in each of the following; %3D 3x +1 if x> 2 x – 1 if x< 2 a) f(x) = %3D x2 if x < 2 b) f(x) = < 2x if x> 2 %3D if x = 2 c) f(x) = * + 5 if x> 2 x3 if x < 2

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Let if a < - 5 if -5 < x < – 1 3 if -1<x < 3 f(x) = if a 3 and g(2) = / r(e)dt Determine the value…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: Find the domain of the function f(x) = /2x – 3 - In interval form, the domain of f is

A: here function is given in form of square root this can't be negative so the value inside is positive…

Q: 2. Given the graph of y = f(x), on the same grid sketch the graph of y=-2f(3x) 5 -5-

A: We see is given graph in question.

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

A:

Q: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

A:

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: What type of discontinuity occurs at x = 1 for the piecewise function? if x <1 if 1<x 3+ x h(x) =…

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Q: Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? […

A:

Q: 1. Examine the continuity of the fiunctions given below: (a) f(x)=x -5atx 2 (b) f(x) =2x +7atx 0

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Q: 4. Graph the piecewise function 3 if -1 2

A:

Q: 6. Graph the piecewise defined function. 1x+4] if x2

A: We will make a table for each piece of the function y=|x+4| , x &lt; -3 x -3 -4 -5 -6 y 1 0 1 2…

Q: (B) Test the continuity of the following function: (3 Marks) (5x +3 f(x) = }2x2 +5 - 5x + 3 ;x< 2 ;…

A: F(x) is not continuous at x equals 2 and 4, and continuous at all other real numbers.

Q: 5 - x, -1sxS 2 r² – 1, 2<x < 3 Discuss the continuity of g(x)

A:

Q: Q1) Check the continuity of the given function at the given c (or c's). 2-4z+3 if I+ 3 { (a) f(x) =…

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Q: Identify any points of discontinuity for the following functions. Indicate if the discontinuity is…

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Q: Let f(x) = ²-7x-18 ✩ if x = -2 if x=-2 Is f continuous at x = -2?

A: A function is said to be continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(a)…