(i) Discuss the continuity of the function f(x)= x^2-3x        if x<2                                                                           2x+4            if x ≥ 2 on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2. (ii) An efficiency study of the morning shift at a factory indicates that an average worker arriving on the job at 7:00am will have assembled f(x)= x^3+6x^2+15x units x hours later. approximately how many units will the worker assemble between 8:00 and 8:15am?

Q: For f(x)= -x^2+4x-3,x ≤ 2, Find f^-1(x) and state the Domian and Range of f^-1(x) and sketch the…

A: fx=-x2+4x-3,  x≤2 Now let y=-x2+4x-3. Now to find inverse function, interchange x and y, then solve…

Q: Draw the graph of f ( x ) = ( − x + 1 ) ^2

A: F(x) (-x+1)2

Q: Suppose the function f is updated from f(x)=x^3 to f(x)=−3.5x^3. How does changing the coefficient…

A: There are two big changes you introduced to the function when you change the coefficient from 1 to…

Q: if g(x)=3x+4 determine n such that g(-3)=g^-1(n)

A:

Q: 8)If f(x)=x/(x-1)^2, f(x)=(x+1)/(x-1)^3 f"(x)=(2x+4)/(x-1)^4 Graph this function using all available…

A: Given function is: fx=xx-12 A function is sad to be undefined at a point where its denominator…

Q: Sketch the graphs of two distinct functions with the property f′(x)=−x^2+x

A:

Q: Find the range of these functions 1. y=(x+2)/(x^2-4) 2. y=√(x^2-x-2) 3. y=(15-x)/(x^2+3x-4) 4.…

A:

Q: If P(t) = 2 and h(t) = 1+3t, compute the following functions and values. If your answer is a number,…

A: Given that : P(t) = 2t and h(t) = 1 + 3t

Q: When doing composite functions, if I have a problem that says f(x)=x/x-5 and g(x)=-3/x/ How do I…

A:

Q: What is function's long-run behavior? f(x)=x-6/x^2-16

A:

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.