The piecwise function g(x) is defined by x + 2 when x < 0, 2x2 when 0 is less than or equal to x and 1 is greater than x, and 3-x when x > 1. What type of discontinuites are present in the function? Where are these discontinuities?

Q: Find a function in general form with a vertex at (-1, -2) and passes through (3, 6). Hint: Start…

A:

Q: Prob. 5 (a) () Find all points where f is discontinuous. Classify these points (if any) as removable…

A:

Q: Consider the following function and closed interval. g(x) = (x² – 9)²/3, [-5, 4]

A:

Q: Determine the point at which the function f(x) = = '? Removable Jump Infinite None of these 1.…

A: We can find where the function is discontinuous.

Q: |x| 3 +x* 2) Without making use of a graph show that the function f (x) is even.

A: Hera function is given and we have to prove that given function is even

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

A:

Q: Prove that a function of the form:is an even function.

A: The given function is  y=a2nx2n+a2n-2x2n-2+...+a2x2+a0

Q: Use the piecewise-defined function to find the following values for f(x). 1-4x if xs-2 f(x) = 4x if…

A: Consider the given piecewise-defined function, fx=1-4x       if x≤-24x             if…

Q: 7x – 1 Determine in which interval(s) the function h(x) is continuous. Justify %3D x2 +1 your…

A:

Q: B. Determine the function which coincides with f(x) for all values with the exception x = 5. (x² -…

A:

Q: ii) f(x) = x*-1 %3D x²-1

A:

Q: Define Į æ² – 5 2x + 1 - 5 if x 1 f(x) = Is there an open circle or a hole on the graph of this…

A: for this function, the value of x should be less than 1  which means there can be a hole at x=1 so…

Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

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.