53. Graph h and describe the discontinuity: for x <0 et h(x) = In x for x > 0 Is h left- or right-continuous?

Q: Q 1: Explain the differences between continuity and uniform continuity with the help of examples…

A: Continuity is defined for the given function at a point but Uniform continuity is a property for…

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A:

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A: Here the given graph

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A: A discontinuity wherein the curve appears to the eye, to be continuous, but the single point  is…

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A:

Q: 2, if x -1 Find the value for a and b such that f (x) = {ax + b, if – 1 3 for all real numbers.

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=-1 so we…

Q: 9) State the intervals of increasing and decreasing behavior in the function k(x) = x2 In x?.

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Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

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Q: Give an example of a function ƒ(x) that is continuous for all values of x except x = 2, where it has…

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Q: Let f (x)=x²-2x + . Find the slope of the graph y = f(x), at point P- (0,7) evaluating th'e limit AX…

A: fx=x2-2x+1 We need to find the slope of the graph at the point P0, 1

Q: 85. Suppose that f is the differentiable function show panying graph and that the position at time t…

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Q: Draw, on your own axes, a possible graph of the curve y = f(x) where f(x) must satisfy the following…

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Q: 4. Explain what it means for a function f to be continuous at a point x = c, with a sentence that…

A: Given: We have to explain about function f  to be continuous at a point x=c

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

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: Find the indicated one-sided limits, if they exist.

A: Find the indicated one-sided limits, if they exist.     fx=-x+6 ,   if x≤05x+5  ,   if x&gt;0

Q: 36. Find constants a and b so that each of the following limits is true. Va + bx lim 1 2

A: Given, limx→0a+bx-1x=2 As, Denominator of the limit tends to 0,numerator should also tend to be 0…

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A:

Q: Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph…

A: To find slope of normal of f at point x=4 from the graph of its derivative.

Q: 5. This is the graph of h. What is the reasonable estimate for the limit of h at x = 3? А. 2 В. З С.…

A: We know that for a function f(x) limx→af(x) gives the value to which f(x) approaches when x…

Q: 2. In a population of N = 10 scores, the smallest score is X = 8 and the largest score is X = 20.…

A: According to the provided information, the smallest score is 8 and the largest score is 20

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

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Q: 2. Below is e graph of f(r)- Let 7'(r) On whiat intervals is inereasing? Decreasing? How do

A: →Newton-Leibnitz rule says that,     ddx∫g(x)h(x)f(t)dt = f(h(x))dh(x)dx +  f(g(x))dg(x)dx→Let F(x)…

Q: True or false? The limit of 1/x as x approaches zero is zero.

A: The given statement is false. Use the property of limits to solve the limit.…

Q: 9+- Find the limit of f(x)= as x approaches oo and as x approaches 8. x² 8.

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Q: If a box with a square cross section is to be sent by the postal service, there are restrictions on…

A: volume of the box,V(x)=x2104-4x

Q: valuate the limit 8x2 – 9x – 9 lim x→-o 7 – 7x – 10x2 E the limit does not exist enter DNE. imit =

A: We have to find limit

Q: 6. True or False The graph of the function f(x) = x? is increasing on the interval (0, ). (

A: f(x)=x2

Q: 2. Use limits to describe the types of discontinuities at x = 1 and x = 3. Justify your work by use…

A: There are a total of 3 discontinuities: Point/Removable Discontinuity, Jump Discontinuity and…

Q: 6. 4 -6 -4 -2 -2 24 6 -6 -4 -2 -2 4 6 -4 -4 -6 -6 (a) Graph of f (b) Graph of g 2. 2.

A: Refer to the graphs given in item 2. Determine the interval/s where f and g are continuous. Identify…

Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: Find  limit x 0  1/x^2if it exists.

A: We find the limit numerically

Q: 6x – 6 if a 4 Show that f(x) has a jump discontinuity at a = 4 by calculating the limits from the…

A: Let fx=6x-6if x&lt;41x+4if x≥4 To show that f(x) has a jump discontinuity at x = 4.

Q: ind the limit as x approaches two of (2x + x – 10)/(2 – x)

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Q: When a function's y-value approaches either +00 or -00 as x approaches c, the Limit Does Not Exist…

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Q: 3. Find the interval fconvergence of the Sevies : 1-3(x-4) + 9 x-4)-..

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Q: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

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Q: Is the discontinuity at x= 0 in the given graph removable? Explain. 101 8- 41 -10-8-6-4 246 8 10…

A: Given, graph of a function having a discontinuity at x=0

Q: find the limit f(x)= (5-x)/x2-25 a) find the x values at which discountous b) which…

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point, take…

Q: Question 4

A: The condition which should be satisfied for continuity,

Q: Suppose f'(x) < 2 for all x 2 2, and f (2) = 7. Show that f(4) < 11.

A: Given that f'x &lt;2 for all x≥2 and f2=7.We need to show that f4&lt;11.

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: [6 – 2x, \x² - 8, xS 3 x > 3 f(x) Where are the intervals where the function is continuous? Are…

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Q: 8. Find the area of the triangle formed by the x and y-axes and the tangent to the graph of y =. %3D…

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Q: II. Evaluate each of the following limits. ArcTanx — х 1) lim x→0 х3 Тапх 2) lim (#- x)таnx — х)…

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Q: 9. Sketch the graph of the following functions and the indicated limit if it exists. Determine if it…

A: The given function,f(x)=x+3if x&gt;22x+1if x≤2

Q: 16. Using the limit as h goes to 0, find the slope of each of the following: a) ƒ(x) = −6x² + 7x − 3…

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Q: 8. Sketch the graph of the following functions and the indicated limit if it exists. Determine if it…

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Q: 3. Determine the value of k for which the function will have a limit on (-∞,). x+2 x<3 2 f(x) = 3.…

A: Given function is : fx=x+22  , x&lt;312-kx3 , x≥3 To find the value of k.