Problem. (problem 10) Determine whether the function f(x) given below is continuous at a = 1. 22 for æ <1 f(x) = for æ = 1 z +1 for æ > 1 f(1) lim f(x) = lim f(x) = ?

Q: * -x+1 if x1 (a) The value f(1) does not exist, while lim, 1 f(x) exists and equals 1. Doth f1).

A: f(x) = x3-x+1 if x&lt;1        = 1/x        if x&gt;1 Since the function f(x) is not defined at x= 1…

Q: I need help with number 51

A: By algebra of limits , we have the following result

Q: 1. lim f(x) = NE Tim f(x) = 2NE lim f (x) = DNE f(1) = DNE. 4 3 X-1 2 3. 2. lim f(x) = 2. lim f(x) =…

A: yes,all these answer are correct

Q: 11) In Problems 11 and 12, given f(x) and g(x ) are continuous everywhere with the values: 2 X =…

A: A detailed solution is given below.

Q: Problem 3.10 Evaluate „1000 1 lim x→1 1 -

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Q: Given the function f(x)=−2x^2 1) Find the difference quotient f(x+h)−f(x)/h 2) Find f'(x) by…

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Q: Problem 8. A function and its first and second derivative are given 2(2x + 11) f(x) = x² - 4 (x +…

A: As per guidelines, I can answer maximum three sub parts of a question. Here are four sub parts, so I…

Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: Sin tan = Cos Problem 2, For each of the following functions f(x) evaluate lim-+0 f (x). Then…

A: Given the function

Q: Problem 02: (a) Graph the following function f (x) and g(x) (b) Investigate whether limx¬1 f (x) and…

A: SolutionGraph of the function f(x)  and g(x)investigate the limit   limx→1 f(x)  and limx→1 g(x)

Q: Problem 3. Using Table 1, reproduced below for cordiality, 3 4 5 f(x) f'(x) | f"(x) 0 1-1 -3 1-1 4 3…

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Q: Solve the problem. 1) If lim f(x) = L, which of the following expressions are true? x-0 I. lim f(x)…

A: Solved below

Q: Problem 2.7 Let Find the limit lim f(x). x 0 f(x) = x² if x is rational 0 if x is irrational.

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Q: 4. Sketch the graph of a function that satisfies ALL of the following conditions: • D: {x ER | x# 4}…

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Q: Problem 2 (Exponential as the limit of Geometric) Let Y - Geometric(p), where p = \A. Define X…

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Q: 5|2 X 1 If f(x) = X A. f(x) is continuous at x = 2 B. f(x) is discontinuous at x = 2 C. lim f(x) = 1…

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Q: Questions 15 - 16: The table below gives selected values of a twice-differentiable function f(x). -7…

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Q: 1. True or false. (a) For a differentiable function f, f'(x) gives the slope of the tangent line at…

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: Problem 1 (2 point) Show that if f is continuous and positive function on [0, 1] (i.e., f (x) > 0…

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Q: Problem Set B 2 x +x-5 (1) Find lim 3 x→> 1-2x-x

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Q: Problem. (problem 11) Determine the value of k that will make the function f(x) given below…

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Q: Problem 1 (Continuous functions). Recall that a function f is said to be continuous at xo if lim…

A: Given, f and g are continuous function at x0. then, for ε2&gt;0, there exist δ1 such that…

Q: In problems g-i, assume a is an integer such that –3 < a < 3. d) lim f(x) = x→a¯ e) lim f(x) = x→a+

A: For the given graph of f(x)g need to solve part d and e;Given; 'a' is an integer such that-3≤a≤3

Q: 17. f(x) * g(x) if x s1 L(x) = x+k if x >1 and limx¬1 f(x) = 3 and limy¬1 g(x) = -5

A: see below the answer

Q: * PROBLEM 3 Vx-4 3 lim x→13 \13-x Evaluate analytically the х-13)

A: Given:

Q: at Let L-1 (F(p); x) = f(x). If f(x) is sectionall lim f(x) exists, then for p > a, we have x→0 x…

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Q: (a + h) - (a) lim- If =b h , where b is a finite constant, then the function y= a. - f(x) has a…

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Q: 2. lim f(x) = | x-1 lim f(x) = 1 x1+ lim f(x) = | f(1) = |

A: 2.According to graph limx→1-fx=1limx→1+fx=1limx→1-fx=limx→1+fx=1there fore limx→1fx=1    limit exist…

Q: f(x)= x^3-16x 1) find a formula for the slope of the tangent at any x-value using lim(h—0) of…

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Q: Problem 6 The Sandwich Theorem for functions of two variables states that if g(x, y) < f (x, y) <…

A: The solution are next step

Q: I need help with number 42

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Q: Question 18 x²+ 2x – 3 if x2 2 The value of lim f(x) if f(x) ={ 6-x x-2 if x<2 2 A) 5 B) 2 c) 3.5 D)…

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Q: Problem 2, For each of the following functions f(x) evaluate lim,-+00 f (x). Then determine the…

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Q: Questions 15- 16: The table below gives selected values of a twice-differentiable function f(x). -7…

A: 15. Consider the table: f-7=0……1f'-7=3……2   To find: limx→-2f3x-1x2-4……3

Q: Problem 3: Given the function g(x) 1 x3 4x-3' Evaluate the following limits: lim g(x), im g(x). im…

A: The given function,g(x)=1x+3,x&lt;-112x2,-1≤x&lt;314x-3,x&gt;3

Q: 19) In Problems 19) through 21), given a piecewise function: |(1- tanx)cot x f(x) = 3/ k (x > 0) (x…

A: Given that:

Q: Problem. (problem 9) Determine whether the function f(z) given below is continuous at z = 1. S 2z…

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Q: S (z +3)3 – 2 z < -3 sin (x +3) -3 = Let F (x) = Find lim F (æ). z+3+

A: To find: The limit of limx→-3+Fx. Given: The function is Fx=x+33-2, x&lt;-3sin x+3,    -3≤x.…

Q: 2 i 2 3 4 5 6 1. lim, - f (x) = 2. lim, 2+ f(x) = 3. lim, 2 f (x) =| 4. f (2) = 5. lim, 5- f(2) = 6.…

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Q: 3. limf(x) = %3D 5. Is f(x) continuous at x = Problems 6-9 find the foll (x+h)' – x' lim 6. h h->0…

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Q: Question 14 f Vx sfx)s÷x+ 1for all positive x-values, then what is lim f(x)? x + 4 Selected Answer:…

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Q: y= f(x) y= g(x) -1- 0. lim [f(x) + g(x)] ...X2. lim [f(x) – g(x)] lim [F(x)g(x)] X-1 f(x) lim x-3…

A: Given graph of two functions f(x) and g(x)

Q: x-1 5. lim n0 x+1 f(x) f(x) -1 1 -0.8 -0.35 0.75 0.45 -0.1 0.2 0.09 -0.9 -0.0003 -0.000001 0.0003…

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Q: Question 4 If f(x) = 2x + 5, then using L'hopital's rule lim 0-70) S(x)-1(0) is X+0

A: If f(x)=2x3+5 , then find the limit of (f(x) -f(0))/x3 when x tends to zero.

Q: Sin tan = Cos Problem 2, For each of the following functions f(x) evaluate lim-+00 f (x). Then…

A: Solving question 1

Q: 13) In Problems 13 through 20 given f(x) and g(x) are Continuous and Differentiable EVERYWHERE with…

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Q: Problem 1: Consider a function that is piecewise-defined according to the formula 3(z + 2) +2 -3…

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Q: Problem 6 The Sandwich Theorem for functions of two variables states that if g(x, y) < f (x, y) <…

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Q: Problem 1: Consider a function that is piecewise-defined according to the formula 3(z+2) +2 -3 1 For…

A: Since you have posted a question with multiple sub-parts, we will solve only first five sub-parts…