9. For a function f(x) to be continuous at a point x = c, the following three conditions must hold: i. lim f(x) exists ii. f(c) exists iii. lim f(x) = f(c) The following function has discontinuities at x =-1, x = 1, and x 2. 3 2- -2 -3 a. For which of the three discontinuities (if any, maybe more than one) is the discontinuity because i (above) fails to hold? b. For which of the three discontinuities (if any, maybe more than one) is the discontinuity because ii (above) fails to hold? c. Which of the three discontinuities (if any, maybe more than one) are removable discontinuities that could be removed by redefining the function at the point of discontinuity? 3

Q: Given that f(x) = 2x² +1, find:“ f(x+h)- f(x) f(x+h)– f(x). lim h→0 h h

A:

Q: 1. For each of the following find: I. lim f(x) II. lim f(x) III. lim f(x)

A:

Q: which of the following statements is true about the function             3x-2, if x<2 r(x)=…

A: We have given,            3x-2, if x<2r(x)=     -8      if x=-2             5x+4 if x>2

Q: Sx² 15 a. Find lim f(x). if x + 2 2. Let f(x) = } if x = 2 X→2 b. Find f(2). Is f(x) continuous at x…

A: Proceed as shown below...

Q: 2. Assume all given functions are continuous. If lim (ƒ(x) – g(x)) = 10 and ƒ(5) = −8 x → 5 Find…

A: The objective of the question is to find the value of g(5) given that the limit as x approaches 5 of…

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: For each of the following find: I. lim f(x) II. lim f(x) III. limf(x)

A: I.Given that fx=sinx when x<π6Therefore,limx→a-fx=limx→π6-sinx=sinπ6=12Hence, limx→a-f(x)=12

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: 3. Sketch the graph of a function f such that the following conditions are true: ● f(4) is not…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: