According to each of the following graphs of functions f(x): (i) (ii) Determine whether f(x) is continuous at x = a. Find lim f(x).

Q: Give the equation(s) for a single function, f(x), that satisfies all of the following: lim f(x) =1…

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Q: If x3 f(x) s x for x in [-1,1], find lim f(x) if it exists. X-0

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Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim x) x-2 g(x) y = 1.4(x – 2) y…

A: NOTE: Refresh your page if you can't see any equations. . for the graph f, the equation of the…

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: x3+1 1. lim X→-1 x+1

A: I am attaching image so that you understand each and every step.

Q: 1 1 (b) lim x-0 'tan x e* – 1 -

A: =?

Q: Can f(x) approach a limit as x ➔ c if f(c) is undefined? If so, give an example.

A: Yes .This statement f(x) approach a limit as x ➔ c if f(c) is undefined is correct. We will see one…

Q: If Зx <f(x) < х +2 for 0 <x< 2, find lim f(x). х—1

A: Result used:

Q: given the attached function, find the following limit limh--&gt;0 (f(-1-h)-f(-1))/h -6 -3 -3/2 -3/4

A: Explanation: Given that,  Now find the f(-1-h) put x = -1-h                           Now find the…

Q: Consider the function x + 1| – |x – 1| f(x) Estimate |x + 1| - |x – 1| lim x 0

A: The given function f(x) is:

Q: Find lim f(x) for the given piecewise function. x-4 2x +2 if x 4 If the limit does not exist, enter…

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Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: Determine the following limits: 2x +3 [a] lim b lim 0 4x-4 sin x

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Q: Find lim f(x) for the given piecewise function. X6 2x + 1 if x 6 If the limit does not exist, enter…

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Q: For Exercise evaluate each limit by first converting each toa derivative at a particular x-value.

A: limx→-1x29-1x+1 On simplification, we get limx→-1x29-1x+1=limx→-1x29--129x--1 Now it is in the form…

Q: If a function is defined at a, but lim f(x) does not exist, how is x→a this shown on the function's…

A: If the limit of a function f(x) does not exist at a, then the function is not continuous at a and…

Q: Each limit represents a derivative f '(a).       Find f(x) and  a.

A: limh→ 05+h3-53hSimplify:=limh→ 0h2+15h+75Plug in the value h=0=02+15· 0+75=75

Q: Use the definition of the derivative to evaluate the following limits.

A: Derivative of a function f(x) is defined as, f'(x)=limh→0f(x+h)-f(x)h. Derivative of a function f(x)…

Q: Complete the following tables of values to investigate lim x→0 x − 1 x + 1 .

A: Consider the function fx=x-1x+1. Compute the value of the function for random values and then make a…

Q: 2. lim x--33 X f(x) ?

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Q: Determine the value of the following limit. sinh(x) = x lim - x3

A: Given that limx-&gt;0 sinhx-xx3

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y4 y = 1.6(x -…

A: We need to evaluate the value of limx→2f(x)g(x) using the following graph

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: Which of the following is the correct limit defihition for the derivative of g(x) = + 4? Select the…

A: Consider the formula for the limit of the  function f(x).

Q: Each limit represents a derivative f '(a). Find f(x) and a.

A: Given, limh→05h-1h

Q: lim (sec x)cot x X-

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Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

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Q: If 4- 3x sg(x) s4 cos x for all x, find lim g(x).

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Q: x3 – 9x + 10 .lim 3 x→2 x2 – 4 4 |

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Q: Find lim f(x) for the given piecewise function. 2x + 1 if x 6 If the limit does not exist, enter…

A: Solution is given below:

Q: According to each of the following graphs of functions f(x): (1) Determine whether f(x) is…

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Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: When lim f(x) exists, it always equals f(a). State whether this statement is true or false. Xa

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Q: Find lim f(x) for the given piecewise function. x-6 2x + 1 if x 6 If the limit does not exist,…

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Q: tanx - x x-0 x - sinx 1. lim

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Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

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Q: Find the following limits when they exist:   1. lim g(x)   x to 3+

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Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: A function is said to be continuous at x=c if limit of function at x=c exists that is limx→cf(x)…

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

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Q: Given f(x) = 5x³ + 7x + 7, write a limit representing the derivative of f(x) at x = −2. Provide your…

A: Given: The function is fx=5x3+7x+7. To find: Value of the limit that represents the derivative of fx…

Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

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Q: The graph of a function f and its tangent line at 0 are shown. What is the value of lim X→0 e7x f(x)…

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Q: Determine the following limits at infinity. f1x2 xSo g1x2 lim if f1x2 S 100,000 and g1x2 S 00 as x S…

A: Given information: The function f(x) approaches 100,000 and g(x) approaches infinity as x approaches…

Q: Determine the following limit. sin x lim x0 X + 16

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Q: Find the relationship between e and s needed to prove S=

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Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

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Q: Given a function f(x) continuous xeR such that lim f(x)+log(1-1)-log(f(x)) = 0, then f(0) is <

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Q: Evaluate each of the following limits. Тапх-x 1) lim х-0 х-Sinх

A: LetL=limx→ 0tanx-xx-sinxPlug in the value x=0L=tan0-00-sin0L=00Therefore apply L hospital…