3 In x if x >1 2 2. Determine if f(x) = is differentiable at r = 1. x² +3 -1, if a < 1

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: #46

A: We need to find the value of b such that the function g(x) is continuous at every x,

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A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

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Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x&lt;1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: 1. Let the function f: R R be given by 1- cos(x) if x + 0, f(x) := if x = 0. 1 Prove that f is…

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: 2. If f is differentiable at a, then Duf(a) = Vf(a) · u. Moreover, if Vf(a) + 0, it gives the…

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

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Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: 2.6. Let ƒ be continuous on [0, a]. If x e [0, a], define fo(x) = f(x) and let %3D 1 fa+1(x) = -…

A: We will use the basic knowledge of integral calculus to answer this question. Note that we can only…

Q: find the critical points:

A: Given function is  and the interval isThe critical points of a function are obtained when the first…

Q: 113. Suppose that F(x) is an antiderivative of f(x) = (sin x)/x, x > 0. Express sin 2x dx х in erms…

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Q: Suppose f and g are both differentiable at a. Which of the following must be true? Select one: O a.…

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Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: 1 Let f(x) = 8 + In (t) dt, for x2 1. Find f'(2).

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Q: (a) satisfies |f'(y) – f'(x)| < L\y – x| for some positive L and every x, y E R. Show that Let f: R…

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

Q: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

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Q: 43. Let f(x, y) = Is it possible to define f(0, 0) so x² + y2 * that f will be continuous at (0, 0)?…

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Q: 4 – x² p(x) = x – 1 at x = 0 Select the correct response: Continuous O Discontinuous

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Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. Prove that h' is not differentiable at x = 0. .

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Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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Q: Assume that f'(c) = 0 and that f'(x) changes from + to - at the critical point x = c. This means…

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Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

A: The given expression is: limn→∞ ∑i=1n 3xi2-5xi+2∆x    on interval [0, 1]   The definite integral  on…

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A: To Determine: true or false                           1) if f'(x)=0 at x=c then f has either a…

Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: Suppose f is a differentiable function with f(7)=1 and f '(1)=- Let y= f(x)·tan x+e* •cos x . Then…

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Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

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Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

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

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Q: Suppose f is differentiable at a and f(a) + 0. (a) Prove |f| is differentiable at a by using that…

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Q: 3. Let f(x) be a positive and differentiable function, and let G(#) = )dt. sf(x)² f(t)dt. f(x)…

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Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

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Q: If f(x)= 2- cos(x) sin(x) , then the absolute minimum of f on the 3T is: interval O 13 O 0 P 2/2-1 O…

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Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: 1. (a) Find when t = 0, if e“ cos t = (x + 1)t + 1. dt2 (Ъ) Suppose f is a differentiable function…

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