11. Give an example of each of the following, or explain why such an example cannot exist. (d) A function f which is increasing on R but not differentiable at 0.

Q: Suppose that f(x) is a function, whose derivative is f '(x)=(1 + cos x)(e* – 1)(x – 2)²(x – 3). At…

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Q: 1) Evaluate the absolute extrema of the following functions on the given interval. S(x)=(x² +3x)³…

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Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

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Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

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Q: 18. Suppose that f is a differentiable function such that f(g(x))= x, and f'(x)= |3D 1 1+(f(x))².…

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Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)>0 then function increasing when f'(x)<0 then function decreasing

Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)>0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: 10. Consider the following function. 1 x } x > Find the values of a and b that make f(x)…

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Q: Determine the values of x at which the function in Figure 18 is: (a) dis- continuous and (b)…

A: (a) Here from the graph, we can see that, The graph has a break at the point x =1, that is, Thus…

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: 8 Check if the following function increase or decrease at given points. f (x) = 3x³ – 6x² + 2x – 1,…

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Q: If W) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

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Q: 2. Consider the function if x = in lowest terms q > 0, p, q € Q; f(x) = O if x e Q°,x = 0 Question:…

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

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Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

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Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

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Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

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Q: (11) (C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on…

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Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x&gt;3 now show that it is continuous at x=3 or not.…

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

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Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Let f be defined by the following. S2x-3 f(x) = 6 - x if x < 3 if x 2 3 (a) Is f continuous at x =…

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Q: Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 2, f’(1) = - 1…

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Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 – 3x on…

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Q: 5. Consider two entire functions with no zeroes and having a ratio equal to unity at infinity. Use…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

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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 with f(0) = 0 and 0 0.

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Q: 20. Determine the following function if continuous at 2x g(x) = \72 – 4x + 3 . ; at x = -1 A.…

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Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.