Determine the values of x for which the function f(x) = {2x 2 − 4   x < 2 x + 2     2 < x < 5 7 x ≥ 5     is discontinuous.

Q: Let h(x) = f(x)g(x). If f(x) = -x – 4 and g(x) = In(2x? – 2x – 4), what is h' (x)? Select the…

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Q: Suppose f(x)=x4+3x+1f(x)=x4+3x+1. In this problem, we will show that ff has exactly one root (or…

A: Solution Given:-         fx=x4+3x+1         Interval -5, -1

Q: 2. Determine with justification, the absolute maximum and minimum of the function below in the…

A: We have to find the absolute maximum and minimum of the function in the associated interval.

Q: Given the following function:  f(x)=(x−1)3(x+2)f(x)=(x−1)3(x+2).  What happens at the zero of x=1x=1

A: We have given function fx=x-13x+2.

Q: Consider the function f(x) - 5æ² – 10x + 0 < x < 10. The absolute maximum of f(x) (on the given…

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 – 4…

A: Given f(x) = x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3 It is continuous if and only if limx→2-f(x) =…

Q: 1 Find the intersection point for each of the following pairs of functions. a f(x) = x- 1, g(x) = 2x…

A: Solution: The objective is to find the intersection point of the given functions

Q: Given function f with f'(x)= 4-4x^2 / (x^2+1)^2 and f''(x)= 8x^3-24x / (x^2+1)^3 (a) Given the…

A: Given, f'(x) = 4-4x2(x2 +1)2  f''(x) = 8x3 -24x(x2+1)3 (a) If f is concave up then f''(x) &gt;0 So,…

Q: We know that 1 is a zero of the function  the multiplicity of f at 1 is:

A: The multiplicity of f at 1 is n if f'(n) is not equal to zero.

Q: 2. Find the absolute maximum and absolute minimum of the following function on the given interval.…

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Q: 2. Find the value of k so that the function Sa² + 25 |kæ – 40 is continuous at x = 5. defined by…

A: Given,          The function defined by fx=x2+25    x≤5kx-40    x&gt;5           is continuous at…

Q: If the domain of the function f(x) is {r E R| – 2 < x < 4}, the the domain of the function g(x) =…

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Q: The function f is defined as f(x)=(x−5)/(x+3)^2 Answer the following questions without using a…

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Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: 6. Determine all values of x at which the function is discontinuous. x2- 2x +5 f(x) = x2-4x 0, 4 O…

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Q: (i) Discuss the continuity of the function f(x) = {x2²− 3x        if x &lt; 2           2x + 4…

A: We are entitled to solve one question at a time, so I am providing solution for first question.…

Q: 2. Refer to the given functions s, t and v to find the indicated function, and write its domain in…

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Q: Consider the following piecewise function where c is a constant real number. Зx2 + 5с х 2 3x2 + 5c x…

A: For limit to be existing both left side limit and right side limit should be equal

Q: In this problem you will use Rolle's theorem to determine whether it is possible for the function…

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Q: - 16 if x 5 Determine if the function g(x) = VX + 4 %3D 5 - x a) x = -4 b) x = 5

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Q: Suppose that g is a function that is differentiable at x = 4 and that g(4) = -2 and g' (4) = 1. Find…

A: We are asked to find the value of h'(4)

Q: Given that f(x) =x+2 and g(x) = x^2 - x find (f+g) (-3) if it exists

A: The given function:

Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…

Q: 3. Determine whether x = 2 is the x coordinate of an extremum of this function: %3D f(x) =- 1 x³ +…

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Q: If g is the function given by g(x) = 1/3 x^3 + 3/2x^2-70x+5 on which of the following intervals is g…

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Q: Find all values of x for which the function f(x)=(x^2+x-6)/(x^2-5x+6) is not continuous.

A: We will solve the problem.

Q: determine all values of x at which the function is discontinuous: 1. f(x)=2x/(x^2-1) 2. f(x)=…

A: Given function is  fx=2xx2-1 The function fx is undefined when x2-1=0 which gives x=±1. So, the…

Q: Suppose thatƒ (1) = 2, that f ' (x) is the function shown in the graph below, and that k (x) = f…

A: Equation of tangent line : y - y0  = m ( x - x0 )  m is the slope of function . And ( x0 , y0 ) is…

Q: Find the values of the constants k and m, if possible, that will make the function f continuous…

A: f(x)=x2+5                x&gt;2m(x+1)+k      -1&lt;x≤2   2x3+x+7        x≤-1limx→2+  x2+5…

Q: If f(x) is a concave function such that f(x) ≥ 0 for all x then g(x) = ((f(x))1/2 is a concave…

A: We have to evaluate that, '' If f(x) is a concave function such that f(x)≥0 for all x then…

Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the open…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Which of the following is a true statement about the function f(x) = 2x³ – 15x² - on the interval 0…

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Q: 11. Decide algebraically if the functions given below are even, odd, or neither. a) f(x) = -7x - 3x3…

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Q: The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4 is:…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 2 Consider the function f(x) = 5x - 6x + 6, 0 < x < 8. The absolute maximum of f(x) (on the given…

A: For maximum or minimum f'(x)=0

Q: Let h(x)=f(x)g(x) where f(x)=−3x2+4x−1 and g(x)=−x2+4x+3. What is h′(4)? Do not include "h′(4)=" in…

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Q: On what interval is the function x^3-4x^2+5x concave down

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Q: If the function f (x) = {_ 4x + 8, x3 is continuous at x = 3, then the value of k is O a. -2 O b. -6…

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Q: Please show step-by-step solution

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Q: If f(x) = |x| + |x – 1| and g(x) is the piecewise function defined by: 2r-1 x> 1 0<x<1 1- 2r x<0…

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Q: Let f(x) = 1 and 1 if x > 0 g(x) 8 +- if x < 0 Show that f'(x) = g'(x) for all x in their domains.…

A: Given,The function g(x)=1x Consider only the case when x&lt;0 because already know that f(x)=g(x)…

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: Find all points on the graph of, for which f′(x) = 0 and those for which f′(x) does not exist.

A: Given: f(x) = x2-123  To find: The points on the graph for, which f'(x) = 0 and those for which…

Q: For what value of the constant 4 is the following function continuous for all real x? if x<1 [ 4x +…

A: From the given x values , we can see that the function f(x) is continuous at x=1 At x=1 the value of…

Q: Which of the following is a true statement about the function f(x) = 2x 15x? on the interval 1 < x <…

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Q: For what values of the constant c is the function f continuous everywhere? f(x)={ cx^2-4x if x<-2…

A: The given data is: fx=cx2-4x, if x&lt;-25x3-c2x, if x≥-2 To find the value of c if the given…

Q: If the function defined by 4x + 64 g(x): x # -16 is x + 16 k x = -16 continuous at a = -16, then the…

A: given function

Q: Show that the following functions has a solution on the indicated intervals. 1. f(x)= 4x³ - 6x² + 3x…

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Q: If the function defined by 6x + 144 x # -24 g(x) = x + 24 k is continuous at x = -24 x = -24, then…

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Q: Show that the following functions has a solution on the indicated intervals f(x)=x³ + 2x = x² + 1…

A: solution:- f(x)=x³+ 2x =x² + 1,      x∈ (0,1)f(x)=x³+ 2x -x² - 1=0Intermediate value theoremf(x) 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.