4 3 2 1 -5 -4 -3 -2 -K 2 3 4 5 -2 -3 -4 -5

Q: Consider the function f (x) = 2x² – 11x + 16. - Express the area under the curve of f on the…

A: This is the integration in the form of summation problem

Q: Lim ex %3D メーo0 x Zero (2) Limit function not Existinge @not of the above

A:

Q: Axample 2 3. Use the definition of continuity to prove that the function is not continuous at x =-5.…

A: Given query is to prove that function is not continues at x = -5.

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

A:

Q: Sketch the graph of a continuous function on [0,2] forwhich the right endpoint approximation with n…

A:

Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: Fill in each blank so that the resulting statement is true.

A: We know, A function f is continuous at a when three conditions are satisfied. f is defined at a,so…

Q: 3. Determine f(x) = x +x-2 is continuous on the given interval (-0,+0) (show graph and its table of…

A:

Q: Suppose that the increasing function ƒ(x) is smooth for x >= 0 and that ƒ(0) = a. Let s(x) denote…

A: Given information:

Q: If it is continuous, there are 3 conditions needed to be satisfied: i. f(a) is defined ii. lim x→a…

A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

Q: If f is differentiable on an open interval containing 0 with lim f(x) f(z) = 0 and lim f'() = 2,…

A:

Q: A Discontinuous Derivative Use the limit definition to show that g'(0) exists but gʻ(0) # lim g'(x),…

A:

Q: 8 - x2 if a 1 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A: Find limit by putting value

Q: II. Given: sinh r − 1 if x 2 x-2 Determine if f is continuous or discontinuous at x = 0 and at x =…

A: Jump discontinue of the function

Q: V. Show that Зx? — 6х — 9 lim 3- х X-3 Is continuous or discontinuous at x = 3

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit and fa are equal and…

Q: ((x + 3)2;x 1 f(x) = %3D 1. lim f(x) = x--5- 2. x→-5+ lim, f(x) = %3D 3. lim f(x) = %3D x--5 4.…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: Given fx=x+x-8,  8,∞

Q: Suppose that f (x) is known to be continuous, and the graph of ƒ (x) on [a, b] has no • corners •…

A: Problem is based on definition of continuity and differential

Q: If f(5)-0, then which of following must be true? fis continuous at x-5 f has a horizontal tangent…

A:

Q: ppose we know that f(x) is continuous and differentiable on [2, 14], with f(2)= -5 and f'(x) <= 10.…

A: Given data:   The given interval is [a,b]=[2,14]. The given value of f(2) is f(2)=-5. The given…

Q: 9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) 0 on…

A:

Q: Let x 2. -3x, f(x) = 1, 3x, Find the indicated one-sided limits of f, and determine the continuity…

A:

Q: 3. Let f(x) and let a>0. Using the definition of the derivative 2+Va as a limit, find f'(a). Your…

A:

Q: Find the limit. 2+5x+ sin x lim 3 cos X 2+ 5x + sin x lim | (Type an integer or a simplified…

A: To findlimx→ 02+5x+sinx3cosx

Q: A function f(x) is continuous at x = c if lim f(x) = f(c). if x + 0 Consider the function f(x) :…

A: The given function is                            fx=xx    if x≠01       if x=0

Q: Find all points of discontinuity for the following: = {x² + 1, x # 0 0, x = 0 Discontinuous at x = 0…

A:

Q: Sketch the graph of a function on the interval [-3, 4] that has the given properties: • An absolute…

A:

Q: A function is defined by: In( x- 1) f (x) =- 1-x a) Using L'Hopital's rule, show that: lim f (x) =0,…

A: Critical points

Q: xãy – xã lim (x.y)-(0,1) x³ + (y – 1)*

A: Solution...

Q: Suppose f " is continuous on (-∞, ). (a) If f '(-5) = 0 and f "(-5) = 5, what can you say about f ?…

A: Given:

Q: If lim f(x) and lim f(x) exist but are not equal, then x = c is a(n) jump discontinuity. X-C- XC+ If…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A:

Q: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

A:

Q: It is possible that functions f and g are not continuous at a point x0 but f+g is continuous at x0.…

A: Given that f and g are not continuous at a point but f+g is continuous at x0 . This statement is…

Q: ILa function f is not defined at x = a then the limit lim f(x) as x approaches a never exists.…

A: Given:If a function f is not defined at x=a then the limit limfx as xapproaches a never exists To…

Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

A:

Q: Sketch the possible graph of a continuous function, f, that has domain [-3, 3], where f(-1)=1 and…

A: Here We use First derivative test to determine the nature of f(x)

Q: Show that f is continuous on (-∞, ∞). S1 - x2 if x s 1 f(x) = In(x) if x > 1 On the interval (-∞,…

A:

Q: a) f(a) exists b) f(x) is defined for 0a f(x) exists e)lim x-->a f(x)=f(a) which ones are true?…

A:

Q: Define limit of a function g(x) at x = a. 3+2x for -sx<0 for 0sx< |-3-2x for x 2 Given, f(x) = 3-2x…

A:

Q: Note that f is continuous on (-o, 2) and (2, 0). For the function to be continuous on (-∞, o), we…

A: First, we find left limit. limx→2-f(x)=limx→2-cx2+3x=c(2)2+3(2)=4c+6 Next, we find the right limit .…

Q: ). Determine the interval(s) on which f(x) =4x−12x−1is continuous. b). Find lim x→0…

A:

Q: in this problem we show that tne function 4x2 – y f(x, y) x2 + Y does not have a limit as (x, y) →…

A:

Q: draw the graph of a function on [0, 5] with the given properties. 1, but lim f(x) and lim f(x) exist…

A: Let us assume that: So, f(x) is not continuous at x=1

Q: if x 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x→ - 3-…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A:

Q: It f:[0,1]→R is a function that achieves a global minimum at 1, and we assume that limx+1- f(x) -…

A:

Q: Sketch the graph of a continuous function on [0, 2] forwhich the right endpoint approximation with n…

A: we have to sketch the graph of a continuous function on the given interval [0, 2]   We have to…

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.