Are functions f(e)= same? why? Explain in foll sentences ang g@): x- the

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

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Q: Describe the long run behavior of f(x) - 2? As x → - 0o, f(x) → ? As x → 0, f(x) → ?

A:

Q: Let f(æ) = (In æ)® f'(x) = f'(e?) =

A: The given function is fx=lnx6. Find the values of f'x and f'e2. Here we use the formula: ddxxn=nxn-1

Q: What are the critcial points of the function f(x) = abs(10x-1)?

A: The given function is: f(x)=abs(10x-1)  or  10x-1 The critical point of the modulus or absolute…

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: Use grahical edition to sketch the graph of f + g.

A: Let the given graphical data be plotted in the form of table x f(x) g(x) f(x)+g(x) 0 1 2 3…

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: What is an even function gine the Symbolic/

A: Given that: Even function

Q: Explain why The Mean Value Theorem does not apply to the function ​f(x)=|x| on ​[a,b]=​[−1​,8​]

A: Given function f(x)=|x| on [a,b]=[-1,8]

Q: Let f (x) = | x |. The mean value of f on the interval [-10, 2] is %3D

A:

Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

Q: A composite function always have domainy E R. O Truẹ O False

A: Given : A composite function always have domain y belongs to Real numbers

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: What is the domain of the secant function?

A: Secant function , Sec xWe know        Sec x=1cos xTo find domain Put cos x=0

Q: Check that the function f(x) = x satisfy the hypothesis of mean value theorem or not at the interval…

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Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

A: Given the statement that " Will a function that is differentiable on a given interval always be…

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A:

Q: How many x-intercepts can a function defined on an interval have if it is increasing on that…

A: It is asked to explain the number of x-intercepts can a function defined on an interval have if it…

Q: On which interval is the function f)= -x- increasing?

A:

Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

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Q: What is the value of f' () if f(x) = ; tanx -1 1+ O Option 4 O Option 2 1- 2 にIN

A:

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: The Mean Value Theorem can be stated as follows: Suppose that a function f(x) satisfies the…

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: Consider the function: fx=1x-3. Mean Value Theorem states that if a function is continuous on a,b…

Q: Which of the following functions are continuous? Why do you think they are continuous?

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Q: Use the Second Fundametal Theorem of Calculas to find F'(x)

A: The second fundamental theorem of calculus is as follows.Let f be continuous on [a,b] then,

Q: What is the range of the secant function?

A: For the secant function: y=secx Range is: y≤-1,or,y≥1 Or in interval notation: secx∈ (-∞,-1]∪[1,∞)

Q: Which is the largest interval over which the function shown in the table is increasing?

A: The given function is: To find the largest interval on which the given function is increasing,…

Q: What is the value of f (-)?

A: Given-  F(x)= -8x+4 F(-1/4) means finding f(x) at x = -1/4

Q: Let f (x) = | x |. The mean value of f on the interval [-10, 6] is

A: Follow next step

Q: Let f (x) = | x |. The mean value of f on the interval [-8, 4] is

A: Given,           Let f (x) = | x |.

Q: What are the variety of important types of functions frequently encountered in calculus?

A:

Q: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

A:

Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: Differentiate the given function glu)- In (u+ Vuzti)

A: Differentiate using basic laws

Q: A function fC) is defined as f) = --Sr. What is f(-3)? %3D

A: Explanation of the solution is given below..

Q: The secant function is defined as: O hypotenuse adjacent O hypotenuse opposite о adjacent opposite о…

A: Given that secant function defined as

Q: Describe the long run behavior of f(x) = – x² - As x → – ∞, f(x) → ? V - As x → ∞, f(x) → (? V

A: Describe the long run behavior of f(x)=-x5As x→-∞, f(x)→?As x→∞, f(x)→?

Q: Differentiate the function. f(x)  = In 1/x

A: Given: The function fx=ln1x, To find: The differentiation of given function.

Q: the faloning composte tarcion. tnd an iner farcien u-t and an cuter function rtui uch that y-g Thon…

A:

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc A…

Q: – one function from X into

A:

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =∣x…

A: Mean Value Theorem: Let f be a function satisfying two condition: 1. f is continuous on a,b. 2. f is…

Q: How do I state the numbers and reasons at which f is not diffrentiable?

A: First check whether the function is differential or not. This can be done using the differential…

Q: What are even and odd functions of symmetry? For example f(-x)=-f(x), f(-x)=f(x), Symmetric about…

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Q: find the derviative of the function in the picture  show all work

A: Here, we use the chain rule of derivative that derivative of (f(x))^n is n[f(x))^(n-1)]f'(x) and…

Q: What is the domain of the function f(x) = |x|? 0 (-∞,∞) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

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Q: a) Evaluate f at x = -1,0, and 5. If not defined, explain. {ogentsY

A: We are given the function,                         .

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.