Does the limit of a function depend on how the function is defined at the point being approached?

Q: Use a linear function to approximate the value of the ∛400 with work.

A: The formula of linear approximation is f(a)+f'(a)(x-a)

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: How to form a piecewise function by using linear function?

A: The piecewise function can be formed using linear functions as shown below.

Q: What is the common way to obtain a new function from an existing one?

A:

Q: What is the definition of the piecewise function from the given domain and range: Domain: (-…

A: The domain and range is given as , Domain = (-∞,0]∪2,∞ Range = -∞,4 find the definition of piecewise…

Q: A rancher wants to fence in an area of 2,000,000 square feet in a rectangular field and then divide…

A: Let, l = the length of one side of the rectangular field w = the length of the other side.

Q: What are the limits of function values?

A:

Q: A function and its graph are given. fx) = + 4x - 20x - 20 250 200 150 100 50 -10 -5 (a) From the…

A: Consider the function:

Q: A function and its graph are given. Fx) = + 4x - 20x - 20 250 200 150 100 50 -10 -5 - 50 (a) From…

A:

Q: Explain Limits of Function Values?

A: The limit of a function at a point 'a' in its domain (if it exists) is the value that the function…

Q: A fixed point of a function f is a number c in its domain that satisfies f(c).  In other words, the…

A: Given: A fixed point of a function f is a number c in its domain that satisfies f(c).

Q: y x3 - 2x*-5x + 2

A: Second Derivative Test : Consider the given function f(x) .Find Critical point , f'(x)=0 (say) 'c'…

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

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.