Can someone please help me with continuity? I would like to check my work, I’m a bit confused on the differentiability part

For f to be continuous at some point x = c, you require that

• f(c) exists and is finite, and

• the limits of f as x approaches c from either side match, and their value must be f(c)

For f to be differentiable at x = c, you require that

• f is continuous at c (i.e. the above conditions are all met), and

• the derivative f ' is continuous at c

Without having the graph of f ', you can assess whether the last condition is met by some function by mentally tracing a tangent line to the graph as you get closer to c. If the slope of the tangent doesn't change, then the function is differentiable. This is usually accompanied by jumps or sharp corners in the graph.

Some examples:

• every polynomial is both continuous and differentiable

• the absolute value function |x| is continuous but not differentiable at x = 0

• 1/x is neither continuous nor differentiable at x = 0

(a) Neither continuous nor differentiable

Why? f has a vertical asymptote at x = -2 and f (-2) does not exist. f is not continuous, and therefore not differentiable.

(b) Neither continuous nor differentiable

Why? From the left, f is approaching 2.5, while from the right, it's approaching 5.

(c) Neither continuous nor differentiable

Why? The limits from either side of x = 2 match and are equal to 0.5, but f (2) itself does not exist (which is indicated by the point being a hollow circle).

If the circle was instead filled in, so that f (2) = 0.5, then f would be continuous there, but still not differentiable. Notice the sharp corner. Or, using the tangent-line analysis, the slope of the tangent to the left of x = 2 is negative, but to the right it would be positive.

(d) Both continuous and differentiable

Why? f doesn't have any special features at x = 3 that would suggest it's not continuous nor differentiable.

(e) Neither continuous nor differentiable

Why? Similar reasoning as in (a). There's another vertical asymptote, but the graph shows f (4) = 1. However, the limits from either side of x = 4 are positive infinity, not 1.

Calvin saved 1/4 of the price of the car he wanted to buy which fraction is 1/4 A 2/12
B 5/20
C 2/16
D 5/25

SOMEONE HELP ME SOLVE THis.

What is 22.5% written as a fraction in simplest form?​

What is OB'?

1.5 units
3 units
4.5 units
6 units

You have a problem. You are running out of M&Ms (the candy). Originally, you had 200 small pieces. Last week, you got a little excited and ate 151 pieces of your original amount in one week (7 days). You are determined to last the remaining M&Ms for exactly one more week. If you eat the same amount every day, how many pieces will you be able to eat each day?

Create an equation to show how you would find the number of M&M pieces you could now have each day.
What is the answer to your equation in part 1? What steps did you take to solve your equation?
Please explain how you know your equation is correct.

11.3
Example 3: A person randomly selects one of the four envelopes
shown below. Each envelope contains a check that the person gets
to keep. However, before the person can select the envelope, he or
she must pay $7 to play. Determine the person's expectation for the
following:

Verify that f and g are inverses functions using composition , show your steps

Solve for x in the triangle,round your answer to the nearest tenth

Helppppp!!!!!!!!!!!!

What is the area of the arrow shown

Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. Steve also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents. (10 points)

Solve 3 - x=-9
a. x=16
b.x=12
c.x=-6
d.x=12

A coin is tossed and ​six sided die numbered 1 through 6 is rolled. Find the probability of tossing a tail and then rolling a number greater than 1.

HELPPP ITS QUESTION 17 BTW

Zara want to purches a new shirt for $19.98 and a pair of sneakers for $64.95.She only has $73.17 saved.How much more money dose she need to purchase the new shirt and the sneakers.

A. 158.10
B. 11.76
C. 84.93
D. 11.84
​

60° 2x + 149 degrees​

PLEASE HELP ITS REALLY URGENT

Find the slope of the line that passes through the two points.

Best Buy bought a television for $175. Then,
Best Buy sold it for $360. What percentage
was the markup?

Determine the value of a.

A) 6
B) 70
C) 7
D) 10

How many ways are there to add three positive even numbers to get a sum of 20? Solve this
problem by making a systematic list, then state your solution.

Help!!!!! can you show your work too thanks

joanne is buying a pair of shoes in europe. the length of her foot is 27.5cm

Can someone help me please

please help I have attached a picture

Help I don’t know the answer

According Two data from the 2010 United States Census 83.7% of Americans lived in the metropolitan area suppose maria researcher takes a random sample of 125 Americans and find that 98 live in the Metropolitan area let P hat represent the sample proportion of Americans that live in a metropolitan area what are the mean and standard deviation of the sampling distribution of P hat provide your answer rounded to three decimal places

Part a identify the similar triangles in the above diagram

AN algebraic expression for -8 subtracted from -x is

Find the missing side. Round to the nearest HUNDRETH.
*
10 points
X
240
12
5.34
6.98
O
12.42
5.25

Which students reads the faster rate in your final answer include all necessary calculations