) For a, 3 ER and B > 0, let f(x) ={} x° sin(|x|-#), when x # 0 when x = 0 0, ange of a and B (and justify your answer) such that is continuous at x = 0. exists at x = 0.

Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

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Q: Show that y = sin (1/x) has no limit as x approaches zero from either side

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Q: Let f : R → R be a twice differentiable function such that f" + f = 0. Prove there exist constants…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

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A: Function is said to be continuous at a point x=a, when the function is defined at a and the limit of…

Q: Consider the function f: RR defined by 1 (a) (b) By using definition, explain whether f is…

A:

Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Suppose that z is a function of z and y and that ze y cos z. Find and

A:

Q: Let f : R → R with f(x) = 3x² + 2. Prove that f is differentiable at the point –1 %3D

A: f(x) =3x2+2 f'(x) =limh→0f(-1+h) -f(-1)h        =limh→03(-1+h)2+2-3-2h        =limh→03+3h2-6h -3h…

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

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Q: The principal part for a) 5 b) 2 for xo of f(x) = 2 + 5+ sinx with respect to ↓

A: Given that .Let .We need to find the principal part of f(x) with respect to g(x) as x→0.We will use…

Q: show that the following function analytic f(z) = 4e²+ Sin Z arp

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Q: Use Exercise 69 together with the identitiessin (h + c) = sin h cos c + cos h sin c,cos (h + c) =…

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Q: 1-x The equation of the tangent line for y = at (- 2, – 3) is 1+X

A: AS PER GUIDELINES I CAN ATTEMPT ONLY FIRST QUESTION

Q: Let f(x) = cos x - x. Prove that f(x) is continuous on the closed interval [0,2].

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Q: Show that sin x < x for all x ∈ (0, 2π).

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Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…