26. a Graph of f The graph of the functionf is shown above. Which of the following statements must be false? TA) Hel exists. (B) f(x) is defined for 0 < x < a. is not continuous at x a. (D) lim f(x) exists.

Q: نقطة واحدة If a function is continuous .7 at a point, then its first * derivative may or may not…

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Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

A: Given

Q: 4. Determine whether the functions f are continuous at given points: x+2 S(x) ={ x +x-2 0, x=1 at x…

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Q: 8) Suppose if x 20 f(r) = if x < 0. Identify a function g with domain R such that lim(f +g)(x)…

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Q: Q 6 Show that the function f(x) = 1+x³ -V1 – x2 is continuous on the interval [-1, 1]. (HINT: show…

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Q: Consider the piecewise defined function x² + 2x – 1 if x 0 ° Which of the following statements is…

A: As we know that,  the function fx is continuous at a point  x=a if the left-hand limit is equal to…

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim f (x)= 21 b) lim x-x+1=-5 x3 c) limx =8 x→2

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Q: , if x + -1 -2, if x = -1 Prove that f(x) = {x+1 is continuous at a = -1 by showing the following.…

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Q: 2. Evaluate the following limits. x+ 1, if x 1 c. lim f(x) a. lim f(x) b. lim f(x) x→1+ x→1- X→1

A: Explained below

Q: 14. The graph of f(x) is not continuous at x = 0 for which of the following reasons? I. f(0) is…

A: Given graph is, From the given graph f(0)=5  as x approaches 0 from left side f(x) approaches to -2…

Q: 28 + x³ Let h(x)=- x1 x² + x - 2 a) Find h(1) b) Determine the values of ß if lim h(x)exists c)…

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Q: Which of the following statements about the function y = f(x) graphed here are true, and which are…

A: Since you have asked multiple question here and hasn't specified any question in particular, I will…

Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: 1 Is the function given by f(x) = ! x+1, for x 2, Choose the correct answer below. O A. The given…

A: We have to find

Q: 2. Create a graph of a function which satisfies all of the given conditions. D = {x € R|x # -2} lim…

A: Solution

Q: Suppose we want to determine whether h(x) is continuous at x = 3. So far, we are given the two…

A: We have, limx→3-hx = 6 h3 = 6 To evaluate: The additional information needed which will allow us to…

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Given function is fx=xx. To find whether function is continuous at x=a, where a=0. Solution:   we…

Q: 2. a) Use the (ε, δ)-definition of the limit of a function at a point to show that lim as x→1 (3x^2…

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Q: 02 3 What is lim f(x) for the function f, defined as f(x)= x-1 Does not exist X-1 √x-1 x²+x-2 X-1 if…

A: The given function is  fx=x-1x-1if x&lt;1x2+x-2x-1if x&gt;1 we find the left hand limit at x=1

Q: 20) Is the function given by f(x) ={x² - 4, for x <0 continuous at x = -2? Why or why not? for x 20…

A: solution:-f(x)=x2-4, for x&lt;0-2,     for x≥0check continuty at x=-2Left hand limitlimx→-2-…

Q: 2. Sketch the graph of the function and use it to determine the following limits. (-x + 1 if x 1…

A: We can find the answer as below

Q: A function f is defined as follows: (px2 – 4, = {2x – 1, x 5 8-x., (a) Given that the limit at x = 3…

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Q: 1 Let f(x) According to the definition, 7 4x f'(x) = lim h0 (Enter the limit in reduced form) %3D

A: Givenf(x)=14x-7

Q: (A) Find the following Limits. x + 5 2. limy-3 f (x) if f(x) = }2x²+4 , x 4

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Q: 10. Choose the true statement. (a) If lim f(x) exists, then f(x) is differentiable at x→0 X = 0. 0,…

A: Solve the following

Q: (a). Determine the interval(s) on which f(x) = is continuous. (b). Find lim analytically. 9-1 3 -1…

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Q: - Define the function f:R → R by ƒ (x) = x +1 if x 0 and f (0) = 4. Show that lim,-0 f (x) = 1 and f…

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Q: 4. Use the given information to sketch the graph of the function f. (-2,1)u(1,x) all real except X -…

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Q: If f and g are continuous functions with f(5) = 2 and, lim[2f(z) - g(x)] =5 I5 find g(5)

A: Given: - f and g are continuous functions with f(5)=2 and limx→52f(x)-g(x)=5 We have to find g(5)=?

Q: 1. Use the graph of y = f(x) below to evaluate the following. lim f(x) = lim f(x)= lim f(x) = f(6) =…

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Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?

Q: 37. The function / has a removable discontinuity at z„. Therefore A S(7,) exists B lim f(z) exists C…

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Q: 4x + 1 Let f(x) = x-2 (b) Use the precise definition of the limit (i.e. M, 8) to prove that lim f(x)…

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Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

A: f(1)=2f is continuous at 1

Q: 58. If f(xo, Yo) 3, what can you say about lim f(x, y) (x, y)→(xo, Yo) if f is continuous at (xo,…

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Q: 8) Suppose if r 20 if r < 0. f(r) = Identify a function g with domain R such that lim(f+g)(x) exists…

A: The explanation is as below

Q: 2. The function is called to be lim f (x) = f(a). エ→ロ 3. is a type of discontinuity when the lim…

A: Fill in the blanks: 2. The function is called to be continuous at point "a" when the limx→afx=fa.

Q: Is the function given by 1 g(x) = 4*+1, for x 8, continuous at x= 8? Why or why not? Select all that…

A: We have to check

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: 1 | 1. lim f(x), where f (x) = x→1 x² – 1° f (x) f (x) 1.002 0.998 1.001 0.999 1.0005 0.9995 1.00001…

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Q: True and False. (1) _A function f is continuous at x = a if and only if limf(x) = f(a). y=x² -10x+5…

A: (1) Concept : A function is continuous if the graph of the function is continuous or we can make the…

Q: S2 – x – x² if x 2 - Use a graph to determine the following limits. Enter DNE if the limit does not…

A: The graph is shown below:

Q: 2. For the function f(x) defined by O if z is an integer 1 if r is not an integer f(1) = (a) Sketch…

A: The given function f(X) is defined as, fx=0,  if x is an integer1,  if x is not an integer To sketch…

Q: ƒ(x) = [x] + [−x] teger function [x] is defined by the largest integer that is less es of a does lim…

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Q: X- 2 a lim " +x-6 T0 – x - 4 sin 2x b. lim c. lim x+ 6

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Q: A function y = f(x) is defined and continuous for all x. This function satisfies all of the…

A: Given that the function  y=fx is defined and continuous for all x. Solution (a): According to the…

Q: 9. Consider the following information about the graph of a continuous function m(x): • lim→-0 m(x) =…

A: Given: The function mx is a continuous function limx→-∞mx=-2 and limx→∞mx=2 The sign of m' and m''…