Graph the function  f x =x + sqrt |x|  Zoom in repeatedly,first toward the point (1, 0) and then toward the origin.What is different about the behavior of in the vicinity ofthese two points? What do you conclude about the differentiability of f ?

Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

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Q: f(x) = In(x)

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Q: 2. Graph the function f (x)= x+ Vlx\ . Zoom in repeatedly, first toward the point (-1, 0) and then…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

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Q: Describe the interval(s) on which the function is continuous. f(x) = sec x/4

A: The denominator can not be 0.

Q: Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the…

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Q: 3) Verify Rolle's Theorem for the function f(x) = [-4, 4]. Justify your answer. 5x + 6 defined over…

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Q: Describe the interval(s) on which the function is continuous.

A: Given: fx=xx+3

Q: Is it possible for a function to satisfy f(x) > 0, f′(x) > 0, andf ″(x) < 0 on an interval?…

A: We want function that is: 1. positive on interval I since fx>0   2. increasing on interval I…

Q: 1. Determine and sketch the domain of the function f(r,y) = e2/Vy¬I, What is the range of f?

A: So, given function is    f(x, y) = e-x/y-1     here,  y should strictly be above 1    and then it…

Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

A: Let a function f : A→B thenDomain: set ACodomain: BRange: Values that comes out after putting values…

Q: Sketch the graph of a function f such that f (x) ≥ 0 on [0, 1] and f (x) ≤ 0 on [1, 2], whose…

A: Consider the function Then and The graph of the function is shown below,

Q: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: 2. What is the lilm f(x)?

A: From the given graph in extreme left side we can clearly see that. If x tends to minus infinity then…

Q: Determine if the function f(x)=arctanx is convex downward or upward at the point x=1?

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Q: Find the relative extrema of the function, if they exist. f(x) = 1 %3D

A: Given,          fx=x2+1x2

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

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Q: a) Investigate whether the function f(z) = z is analytical?

A: In order to investigate whether the function is analytical or not, first write the function f(z) in…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: Use the graph of f to find the interval(s) on which f is decreasing., Where applicable, use interval…

A: we have to use the graph to identify where f(x) is decreasing.

Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Describe the interval(s) on which the function is continuous.                            f(x) =…

A: fx=xx2+x+2 Since there is no common factors in the numerator and denominator, therefore there is no…

Q: Determine where the function f(x) is continuous. f(x) = /2-x

A: We have to determine where th function f(x)=(2-x)^(1/3) is continuous

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: X- e.

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Q: x +1 x 2

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Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: Find a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: Determined where the function f(x) is continuous

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Q: Which derivative of f tells us whether the function is increasing or decreasing?What do we check to…

A: Given function ,  f(x) = ln ( x2 + 2x + 5)  Find interval of increasing and decreasing .

Q: Find the intervals on which the function f(x)=x+1/x is convex upward and convex downward.

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Q: Evaluate the piecewise defined function at the indicated values.

A: For f(-2) and f(-1) , the value of x is -2 and -1 respectively , which is less than 0 . So for this…

Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

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Q: Find the domain of the function using interval notation. f(x) = -2x (1- 1) (r – 7) To enter oo, type…

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Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: Describe the x-values at which f Is differentlable. (Enter your answer using interval notation.)…

A: Describe the x-value at which f is differentiable  f(x) = √(x+1)  +1

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: Describe the x-values at which f is differentiable f(x) = √(x + 1) + 1

A: We have to describe the x-values at which f is differentiable fx=x+1+1. We know that a function f is…

Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.

Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: ) Use the Intermediate Value Theorem to show that there is one such that f"(a) = 0. point x = a

A: As per our guidelines we are supposed to answer only first 3 subparts of the question. Kindly repost…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: