1. Determine whether a - 6, if 0 6 is continuous at a = 6

Q: -3 For what value(s) of x is the function f(x) = 2x+4 (x²+x+1 NOT continuous? A. C. x = -2 only x =…

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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)…

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

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Q: 3. State where the function below is continuous using interval notation. if x<2 4 f(x) = 3 if x 2

A: To check whether the given function is continuous using interval notation.…

Q: Determine if the following are functions of x. (a) X y 8 12 16 20 (c) LO y = 5 ---Select--- 0 5 (b)…

A: Use definition of function

Q: 4. TRUE or FALSE: If f(a) 0, then # x-a is a factor of f(x).

A:

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

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Q: Find the value of the constant a that makes the following function continuous on (-∞, ∞). 5x³ + 5x²…

A: We need to find a value that makes the function continuous.

Q: Let 2x - x if 0 4 (a) For each of the numbers 2, 3, and 4, dctcrmine whether g is continuous from…

A: We are given                 . For (a), For each numbers 2, 3, and 4, we need to determine whether g…

Q: 8. Find an injective function from P(N) × P(N) into P(N).

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Q: ii) f(x) = x*-1 %3D x²-1

A:

Q: Suppose that: ={26 3 for x 7 for x 7 f(x) Determine f(7) if f is right-continuous at x 7. (Give your…

A: To determine the value of the function f(7).

Q: 2. A function, f, is called ....if, whenever a + b, then f (a) + f (b). That is, for any two…

A: Here if a≠b then f(a)≠f(b) is equivalent as f(a)=f(b) then a=b

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: 4x-8 i- -2 x +3a

A:

Q: Is the following function continuous? x2 – 9 if x 3 if x = 3

A: The function is given by

Q: Given triangle ABC with vertices A(2,8), B(8,8), C(16,4) and dilation scale factor k=.75,  give the…

A: Given : Triangle ABC with vertices A(2,8), B(8,8), C(16,4) and dilation scale factor k=.75   Note…

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.