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

Q: 8. If ƒ(x) = − x² + x, which expression represents ƒ (x) ? A. −−(x+h)²+(x+h)-(-x²+x) h B.…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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 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: 2. State whether each function in question 1 is continuous or not. If not, state where it is…

A: Definition of the continuous function is, Right hand side limit and Left hand side limit should be…

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: 4x f (x)=- x2 +4 %3D

A: f(x)=-4xx2+4

Q: Find values of x, if any, at which the given function is not continuous. (a) f(x) (b) f(x) = |x³ -…

A: Find the x values where the function is not continuous.

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: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

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Q: Find the value(s) of a and b for which f is continuous at -2: 3x³ - 7x² + 7 if x -2 f(x)

A: To find the values of a and b for which f is continuous at -2.fx=3x3-7x2+7 if x&lt;-2a+b if…

Q: Determine whether the following function is continuous at the given point x = 3x? + 14x – 5 1 x + 3…

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Q: 1 Expand f (z) = in the domain 4 < |z| < 12 (z-4)(z-12)'

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Q: Show that the equation 5 = x has at least one real root. You %3D may assume that the functions 5 and…

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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: ii) f(x) = x*-1 %3D x²-1

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Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

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

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Q: 1.Make a table for n=1,2,3,…,10 to compare the functions f(n)=n^2, g(n)=2^n and h(n)=n! and graph…

A: Make table as needed:  n f(n) g(n) h(n) 1 1 2 1 2 4 4 2 3 9 8 6 4 16 16 24 5 25 32 120…

Q: -4 if x1

A: The given function is: f(x)=-4        if  x&lt;-2(x+1)2-1    if  -2≤x≤1-14x+2if  x&gt;1

Q: 1.) Let f(x) = 7 + What is f(3 + h)?

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Q: C. Evaluale f(?-1) if F()= 3. if 251

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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

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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.