2. The gragh of g is given as following. (a)At what numbers is g discontinuous? Why? (b) At what numbers is g not differentiable? Why? 1

Q: Suppose that the values of a smooth function f are known on [0, 1]. Which formula gives the better…

A:

Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 %3D

A: 7.  There is a removable discontinuity at x=1 and f(1)=4

Q: The function, that is O everywhere except at t=0, is know as: None of these O Unit step O Delta O…

A: topic - functions

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A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose…

Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Sol:- By applying extrme value theorem frection                      has to be continuous on x E…

Q: Consider the following. 1피 < 1 |z| 21 tan f(x) = Find the x-values at which f is not continuous.…

A: f(x)=tanπx4,x&lt;1x,x≥1

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A: To Prove: a. If f is a differentiable function such that f'(x)≤c for every x.Then for any real…

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A: Now we check the continuity at x = 0:

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A: To identify the function guaranteed by the extreme value theorem to have an absolute maximum on the…

Q: 1 Find the interval on which the curve F(x): -Sa di is concave downward. 6+ 8t

A: Solve the following

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A: Introduction: The mean value theorem is an advanced and very important property that a…

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Q: The Harnack inequality explained in the lecture implies that for any ball BR(x4) of R", if u E C²…

A: We know the following definition. Harnack's Inequality: If u is a non-negative continuous function…

Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

Q: Based on your work in part a, on what interval(s) is f(x) continuous?

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Q: for the funclion fln)= 28? 1l, find f (X th)- F(x)

A: topic - functions

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A: Cauchy-Riemann conditions:  The complex valued function  f(z)=u(x,y)+iv(x,y) is analytic if it…

Q: 8. Verify Rolle's Theorem for the given interval by checking f(a)=f(b), then find a value c in (a,b)…

A: Explanation of the answer is as follows

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A:

Q: If we try to apply Rolle's Thorem to the function f(x) = 2x² – 20x – 5 on the interval [0, 14],…

A: Here, the given function is: f(x)=2x2-20x-5 and the interval given is [0,14].

Q: The domain of the function f(x) = arccos(x – 1) is equal to which of the following %3D intervals?…

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Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Fir applying Extreme Value Theorem function has to be continuous on              x € [0, 4]

Q: Which of the following functions of z is guaranteed by the Extreme Value Theorem to have an absolute…

A: Extreme value theorem is applied only to the continuous function in the given bounded interval.

Q: Which of the following functions of z is guaranteed by the Extreme Value Theorem to have an absolute…

A: Extreme value theorem: -  According to the extreme value theorem, if a function is continuous over a…

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A: Given that f has both 0 and 1 in its range.  This means there will be some x and y values for which…

Q: Consider the following. f(x) = tan( Find the x-values at which f is not continuous. Are these…

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Q: , 6]. che function on this interval. 1/sqrtx ow there exists a c in the open interval (2, 6) such tl

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Q: The circles without boundaries in usual topo log y of R² are Open not closed sets O Neither open nor…

A: The given set is the circles without boundaries in usual topology of ℝ2. Now, there are no…

Q: Suppose that f: R → R and g : R → R are related by the formula f (x) = g(x)+(x-a)". For which values…

A: Note: A function fx is tangent to the function gx at a point x=a if (1) fa=ga, and (2) f'a=g'a

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Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

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A: Since f(x) is a polynomial function and so it is continuous on closed interval [0, 2] and…

Q: Which of the following is the formula for the length of the arc, L, of the curve y = f(x) such that…

A: The answer is given below:

Q: A. is definiteand continuous, B. is indefinite and continuou C. is discontinuous and definit D. is…

A: Given: To explain the correct option of the given statement as follows,

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Q: Since the simplified numerator, >0 for all X, we have "(x) > 0 x²-1>0 e ]x > and f"(x) < 0 X| < Thus…

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Q: Consider the following. f(x) sin - {xta (² () <1 ||21 Find the x-values at which is not continuous.…

A: f(x) = sinπx2,|x| &lt; 1x,|x| ⩾ 1 At x = -1 ⇒limx→-1+f(x) = limx→-1+sinπx2 = -1⇒limx→-1-f(x) =…

Q: Which of the following tatements is true about a mooth function f at (a, b) it ² (a, b) c, fax (a,…

A: f has relative maxima at (a, b) if D&gt;0, fxx(a,b)&lt;0 f has relative minima at (a, b) if D&gt;0,…

Q: Find and for the functions: of Əx af ду bren 2. f(x, y) = x² − xy + y² X (x² + ² noitonut sil 4.…

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Q: Consider the following. f(x) = 9x – cos x Find the x-value at which f is not continuous. Is the…

A: 3x  is continuous for all real numbers  x  (we write as  ∀ x ∈ R  which means for all  x  in the set…

Q: to determine if the 5.) Use the function, f cx) = 2 Detinition S x+3 is cont. a+ point of メー9…

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Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…

A: Let f be any function that is not differentiable  at the point a and define as: gx=-fx for all real…

Q: Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and Q(b,f(b)) be…

A: Given information:Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and…

Q: For which of the following functions and domains does the Extreme Value Theorem guarantee the…

A: Check which function guarantee maximum and minimum value on the domain using extreme value theorem

Q: · For what values of x such that 0 < Is 27, does the graph of f(x) = x - tan r have a rizontal…

A: We will solve the following

Q: (2 Assume that finis define and peioclic with s how that if f for au x peiad T, tubegrable n for…

A: assume that fx is define for all x and periodic with period T to show - if fx is integrable in 0≤x≤T…

Q: 4) Let the curve c be given by the graph of the functionm y= {(x) withh tlx) = cosh x, %3D c)…

A: The curve of the function is given by, fx=coshx, 0≤x≤4To compute the length of the curve

Q: From the Intermediate Value Theorem, is it guaranteed that there is a root of the given equation in…

A: