75. Show that if a function f is defined on an interval symmetric about the origin (so that f is defined at -x whenever it is defined at x), then f(x) + f(-x) , f(x) – f(-x) f(x) = (1) 2 2 Then show that (f(x) + f(-x))/2 is even and that (f(x) – f(-x))/2 is odd.

Q: Verify that the Mean Value Theorem applies to the function f(x) = √25-x2 on the interval [-3, 4] and…

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

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Q: 3. Show that the functionf on [-1,1] defined as if f (r) = 1+e if x = 0 is discontinuous at x = = 0.…

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Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x…

A:

Q: 13. Find the end behavior for f(x) =x- 2 A. x- +0, f(x) - +o x--o, f(x) → - B. x +o, f(x) - +0 x--o,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Verify that the Mean Value Theorem applies to the function f(x) = v25 – x² on the interval [-3,…

A: Use mean value theorem

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

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Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

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Q: _25. Determine if f (x) = {"" (2x – 1 if x 5 is continuous on [2,5]. A. discontinuous on an…

A:

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

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Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

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Q: (3) Show that the function is discontinuous on the specified interval. Vx2 - 64 if x < -8 if -8 <x <…

A: Note: According our answering guidelines we have to answer only one question (if there are multiple…

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

A:

Q: How do you solve question 4?

A: We are given the function, f(x) = x4 – 2x2 + 3x. Here, we need to show that the function f(x) has a…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

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Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: To check for the continuity of the function fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

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

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: (b). Find the bound for absolute error at x = 2.9 on the interval [x, x,], where x, = 2.25, x, =…

A: On the interval x0,xn where x0=2.25, x1=2.5, x2=2.75, x3=3 with n=3 along with the function…

Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

A:

Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x²+2x x≤1…

A:

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

Q: Find a function such that f'(-1)=1/2, f'(0)=0, and f''(x)&gt;0 for all x, or prove that such a…

A: Given that f"(x)&gt;0 for all x and f'(-1)=1/2, f'(0)=0 Since f"(x) exists for all x, so we can say…

Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

Q: Suppose f(x) is a continuous on the interval [a,b] and c is a number in (a,b). If f"(c) is…

A: If f(c) is a local maximum then f''(c) &lt; 0 and if f(c) is a local minimum then f''(c) &gt; 0

Q: Show that the function g(x)  =x| x has an inflection pointat (0, 0) but g"(0) does not exist

A: Given: The function g(x)= x |x| For x&lt;0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 5) Show that the function f(x)=-÷+1 below is continuous at x = -1. x-1 2- -3 -1- -2 1.

A: A function f(x) is continuous at x=c if  We have to show that is continuous at x=-1.

Q: 1-What are Univalent Functions .

A: We define a function on complex numbers.

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

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Q: draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

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Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

A: