1. For any function f(x) such that the number a is in the domain of the function, lim,→a f(x) = f (a). True/False? Justify.

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

A: Given- If the function fis undefined at x=c then limx→cfx does not exist. To Check- If the above…

Q: Given the function f ( x ) = 1 /(x + 3) . Find  lim Δx ⟶ 0 (f ( x + Δx ) − f ( x ))/ Δx

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Q: Find the limit of the following function ex (a) lim x0 e1/x+1 (b) lim f(x), where f(x) = { 3x – 2,…

A: To find the limits

Q: Answer the following True or False: If lim f(x) exists, then f(x) is a differentiable function at x…

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Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

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: Let f be a function that satisfies |f(x)|<M_for all x# 0. Show that lim(x f(x))=0.

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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: Given f(x) = 6 x + 1, find f'(x) using the limit definition of the derivative. f' (x)3D

A: Given, fx=6x+1 We have to find f'x using the limit definition of derivative.

Q: Compute f(x +h) + f(x– h)- 2f(x) lim h-0 h2 for the following functions: (a) f(x) =x (b) f(x) = x2…

A: For the real function f, if f(a+h)-f(a)h has a limit, h approaches to zero. This limit is the…

Q: Suppose the line L crosses the y axis at 7 and L is Tangent to a function f(x) at the point (5,3).…

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Q: Consider the function: f (x) · g (x) = 15x · tan 12 What is lim f (x)· g (x)?

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Q: I. Determine the limit of the function, f(x) = 2x – 5, given the graph. 1. lim(2x – 5) = , X2 2.…

A: Given graph of the linear function f(x) = 2x - 5 is as follows:

Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: 1. Show that for all f e L'(R) lim %3D

A: Put the delta = 1 in integral function

Q: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x&lt;1 fx=x-1                             if x≥1 limx→1fx…

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: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: Why is the following function discontinuous at x = 1? (1+x² ifz 1 (a) f(1) does not exist. (b) lim…

A: We have to find out

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: 3. Is lim f(x) always equal to f(c)?

A: Is limx→cfx always equal to fc The given statement is not necessarily true.

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

A:

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: Question: How else might you define "the limit as x approaches a of the function f (x) is L"? 3.

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Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

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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: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

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Q: Evaluate lim f(x+h)-f(x) h→0 for the given value of x and function f. h f(x)= 5x , x= -2 |

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Q: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

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Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: Consider the function f (x) = x(Va – 1), where a > 0, x > 0. If 0 < a < 1, show that limx0f (x) is a…

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Q: Let f(x) be given by x²+1 if x 2 Find lim f (x) X-2

A: Topic = Limits

Q: Evaluate the left hand and right hand limits of the function defined by (1+x, if 0 1 at x 1. Also…

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Q: T is discontinuous at -1 because lim f(x) as x--> -1 does not exist. * %23 .7. 5. %23

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Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: 9 Given f(x): = =, find f'(x) using the limit definition of the derivative. x f'(x)=

A: The given function is fx=9x

Q: * :Test the following function using limits x² - 25 lim x→→5 x² + 2x - 15 B) 5/3 A) 5/4 O C) 5/2 O

A: Apply the following steps to find the value of the given limit. Factorize the expressions in the…

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

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Q: f(x) = 3x 2 − 2x + 1.

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Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

Q: For the function f(z) = 4x + 19z + 28, find f'(x) using the f(x +h)- f(x) definition lim O 8% O 38z…

A: Here we will find f'(x) using the given definition.

Q: Given the piecewise function |x² + 1, if x > c f(x) = | 2æ, 2x, if x <c lim f(x) exists find the…

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