using the definition of continuity and the properties of limits to show that the function is continuous at the given number a.  f(x)= 3x2+(x+2)5, a= -1 can you please explain this problem with work

Q: Complete the table and use the result to estimate the limit. Use a graphing utility to graph the…

A: limx→01-e7x3x Here, fx=1-e7x3x When x=-0.1, f-0.1=1-e7-0.13-0.1=-1.678 When x=-0.01,…

Q: (7) Evaluate the limit of the function by determining the value the function approaches along the…

A: a) ley y=0L=lim(x,y)→(0,0)xy-y3x2+y2L=lim(x,0)→(0,0)0(x-02)x2+02L=0x2L=0b) Let…

Q: Piecewise-Defined Function Discuss the continuity of x for x 3

A: Given:             Fx=x    for x<13    for 1≤x≤3x    for x>3 Fx is continuous at x=1 If…

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

A: Given,          f(x) = (x+3x⁵)⁴

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) =1 a…

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Q: Definition: The definition of “the limit as x approaches infinity of the function f(x) is L"

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Q: [5] Using the limit definition of a derivative, find the derivative of f(x) = x² – x. Show that this…

A: Shown below

Q: Given a function 4 - x2 g(x) 3 - Vx2 +5

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Q: Discuss the limit of the function as x approaches c and the value of the function as x = c.

A: Discuss the limit of the function as x approaches c and the value of the function as x = c.

Q: Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then…

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Q: true or false questions. please explain why.  . 1-if lim_{x->a} f(x)=∞ and y=g(x) is defined and…

A: Bounded below: A function f(x) is said to be bounded below on an interval I, if there exists a real…

Q: A function f is differentiable at a number a You Answered if f is continuous at a. f(x)- f(a) if lim…

A: Given query is to find correct option for the function.

Q: Complete the table and use the result to estimate the limit. Use a graphing utility to graph the…

A: To find:             limx→0 sin xx

Q: f(x) = -2x2-2x+4 is %3D x-1

A: Follow the procedure given below.

Q: Determine whether the following statements are true or false. If true, provide justification. If…

A: If f1=2, then limx→1fx=2. Given statement is false. For example, let us consider a function fx=x2+2…

Q: Example Let f(x) = /x. 1. Find f (x) using the (limit) definition. 2. Find f'(4). 3. Find the…

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Q: Definition: The definition of “the limit as x approaches a of the function f(x) is infinity" is ...

A: Given data is : The definition of the limit as x approaches a of the function fx is infinity. Let…

Q: lim f(x) = 3 x→2* lim f(x) = 0 X-→2 f(2) = 3 lim f(x)= -2 X--1 f(-1) = 1 b. Is f(x) continuous at x…

A: Given thatlimx→2+fx=3limx→2-fx=0f2=3we have to check the function fx continuous or not at x=2.

Q: True or False: If limit as xà0 of f(x) equals zero then f(0)=0. If false provide an illustrative…

A: We will check whether the given statement is true or false.

Q: Complete the table and use the result to estimate the limit. Use a graphing utility to graph the…

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

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Q: (a) Use the limit process to find the slope of the line tangent to the graph of f at x = 2. Slope at…

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Q: Consider the function: f(x) = x³ - 5 i. Use the limit definition of the derivative (First…

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Q: 4. f(-5) = 5. Is the function continuous at x = -5? If not, what type of discontinuity occurs? 6.…

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Q: 2. If not, indicate Given the function below, determine if the function is continuous at the point I…

A: We need to check continuity of given function.

Q: Direction: Check for the existence of the following limits. If it exists, determine the limit and…

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Q: 10. Evaluate the limits using any of the methods you know. Show your work. x-sin x а. lim x-0 tan…

A: We will use the formulas from this data . and

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) 1 f(x) a =…

A: The given function is fx=1x+1. Find why the function fx=1x+1 is discontinuous at the point a=-1 as…

Q: Direction: Check for the existence of the following limits. If it exists, determine the limit and…

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Q: Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then…

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Q: 4. Determine where f(r) is discontinuous. Use the definition of continuity dis- cussed in this…

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Q: Discuss the continuity of the function on the closed interval. Function Interval 1- x, f(x) = { 1 1…

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Q: Let f : R2 -→ R and suppose that lim f (x, y) = -10. (х, у)-(3,0)° What can you say about the value…

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Q: 3x -1 when x 2 Find a value for b that satisfies the requirement for the function to have a limit as…

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Q: lim (x,y)→(0,0) f(x, y) to be along the x-axis. Based on the table of values, enter what you believe…

A: Given: Let us consider the given table of values, Enter what you think limx,y→0,0 f(x, y) is along…

Q: continuous at every number in its domain. State the domain. g(x) = 3r 1 22 + 2x - 15 b), Jse the…

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Q: A rectangular garden will be placed adjacent to a building. It will be enclosed by wooden fences…

A: Given query is to find the correct statement for the situation.

Q: x²-4 x < 2 x-2' ax² - bx + 3,2 ≤ x < 3 a+b, x ≥ 3 2x Explain your reasoning using the three…

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Q: • Find a formula for a function with the tollowing properties and give a sketch of your function.…

A: Define f:ℝ→ℝ by  fx=-1x+1,-6.313≤x&lt;1xsinx, x≤-6.313-0.5,…

Q: Test II. Determine whether the function f(x) x +6x + 9 is continuous at x = -2. Sketch its graph…

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Q: Discuss the continuity of the function on the closed interval. Function Interval 9 - X, f(x) = [-3,…

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Q: Using L'Hospital's Rule, evaluate the limit as x approaches infinity, [ln(x)/√(x)]

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Q: the limit, if it exists. (If an. Vx2 + 25 + 25 – 13 lim x →-12 x + 12

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Q: 5. Find all constants a, b that make f continuous everywhere. (Use limits and definition of…

A: With the help of limiting criteria we have to find the values of a and b.

Q: sin? (x) lim x→∞ x2 + 1

A: Squeeze theorem.

Q: A. Find the limits of the function f(x,., -2 2 1. lim f(x)= x--1+ 2. lim f(x)= X-4- 3. lim f(x)= 4.…

A: The graph of the function is  To evaluate:  1. limx→1+fx2. limx→4-fx3. limx→4+fx4. limx→1-fx5.…

Q: explain and use the definition of continuity and limit value (the “-δ definition”) to display the…

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Q: Limit of a difference quotient Assuming ƒ is differentiable forall x, simplify

A: Here given as L=limx→5fx2-f25x-5 When the limit applies, It becomes 00 form. Thus use I'hospital…

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

A: Given function f(x) = (x+4x5)3 to show funciton is continuous at a = -1A function is said to be…

Q: Definition: The formal definition of “the limit as x approaches a of the function f (x) is L" is ...

A: Given: The formal definition of "the limit as x approaches a of the function f(x) is L" is ______.

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.