Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

Q: Find the values of a and b that make f continuous everywhere. x2 4 if x 3 a = b =

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Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…

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Q: (b) Verify Mean Value Theorem for f(x)= 3x2-6x -5 over the interval[-1,4].

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Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: Find the values of a and b that make f continuous everywhere. x²-4 if x 3

A: If a function is continuous everywhere Then right hand limit and left hand limit on any point will…

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

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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: Express dx as a limit of left Riemann sums but do not attempt to eval- x2 uate the limit.

A: Given, ∫-11-6 5x2dx

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

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Q: Show that f (x) = is not uni form continuous on (0,3) -3

A: To prove that 1x-3 is not uniformly continuous on 0,3

Q: Suppose that ?(?) is continuous and differentiable on the interval [0,6], that ?(6) = −7 and that…

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Q: Find the largest open intervals where the function is concave upward. f(x) = x 3-3x2 - 4x + 5 O None…

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Q: Find the extreme values of f(r) = Vr(5 – x) in the interval [–1,3].

A: For extreme points we need to find critical points and check value of f(x) on boundary values of…

Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

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Q: find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable?

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: The given equation is x4-x-8=0. Intermediate Value Theorem: Let f be a continuous function on the…

Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

Q: is the net signed area between f(x)=2x+2 and the x-

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Q: Iff is bounded and integrable in the interval [a, b], f(x) cos nx dx=0. show that lim

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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: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

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: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

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Q: Find the domain of f (x) = V3-x x(x+2) Use interval notation, "ninf" for -∞, "inf" for oo, and "U"…

A: Given: fx=3-xxx+2   The domain is the set of all x values at which function is defined and real.…

Q: Every continuous function on a, b, that has absolute extrema on endpoints, must have one critical…

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: Show that f (x) =++1 1 - is not uni form continuous on (-1,0)

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Q: Verify mean value theorem for ƒ(x)=x' – 5x+6 over the interval [1,3].

A: Please refer to the image below

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - 4 if x < 2 X - 2 f(x) = ax2 -…

A: Here, we need to find the values of a and b. We are given that f is continuous everywhere.  So,…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

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

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Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: is: The interval of continuity of flx) = /2x – 10 OA[5, +0) OB.(-5, 51 OC(-0, + x) OD(-00,-5)

A: Function f(x) is continuous on interval [a,b] if it is continuous at every point.

Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…

Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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