• This question is concerned with limits and continuity of the function graphed below at a specific set of points. The x coordinates of these points are x = 1, x = 3, x = 4, æ = 5, x = 6 • For each of these points: 1. Write whether the function is continuous or not. 2. If the limit exists, determine it, writing your answer in the form lim f (x) = L where you write the specific values of c and L for that limit. 3. If the limit does not exist indicate that fact. Example. At x = 0, ƒ (x) is discontinuous and the limit does not exist.

Q: Find the limit for the following function, (2 + h)-1 – 2-1 lim h-0 h

A: We use to solve this limit by simplification/factorization method

Q: g(x) = if X²1 if X=1 2-x2 if 1≤ x ≤ 2 X-3 if x >2 X 3

A: Please see the below picture for detailed solution.

Q: 5x lim x→-3 Vx + 4 1

A: This is not indeterminate form so simply put the value of x and simplyfy .

Q: lim x-3 x²2x-3 3-x

A:

Q: 1. Create a table of values and sketch a graph of the piecewise function. 2. Be sure to use the…

A: The given piecewise-defined function, fx=2x-1,x<1x+1,x≥1 We have to sketch the graph of the…

Q: ACTIVITY 1: CONTINUITY AND DIFFERENTIABILITY Direction: Apply the concepts that you have learned…

A:

Q: Find the form of the following limit and evaluate it. Vx +3 – V5 lim X+2- X - 2

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.