Q3) For what values of a and b are -x² + a , x< 0 1 xsin-+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: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

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Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: Find all values of c such that f is continuous on (-, ). 9-, f(x)3= C = (smaller value) (larger…

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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 x - 2 ax2 - bx + 3 if x < 2…

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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: The base of a three-dimensional figure is bound by the line y = 4 - x on the interval [-2, 2].…

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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. 16) f(x) = x3 - 3x2 – 4x + 5…

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, 1]?

A: follow next step

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: Find all values of c such that f is continuous on (-, 0). 7- a?, { x c C = (smaller value) с 3…

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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: Determine if f(x) = x4sin(1/x3) is uniform contuinius in the interval f : (0,∞) --> R

A: Some facts related to uniform continuity of function: A  function f is uniformly continuous on…

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

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Q: 3. Determine the largest interval where j(x) = Vr² – 1 is continuous.

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

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Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: Left- and right-continuity a. Is hlx2 = Vx - 9 left-continuous at x = 3? Explain. b. Is h1x2 = Vx -…

A: To Determine: find left hand and right hand continuity at x=3 and explain this Given: we have a…

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

A: Please refer the attached image for complete solution.

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: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 1+x² * (Use decimal notation.…

A: Given: f(x)=81+x2

Q: . Find the maximum value of f(x) = In(x – In x) on the interval -sxs. Show all steps .

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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: 4x-8 i- -2 x +3a

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Q: Find the largest open interval using the tools of calculus where the function is changing as…

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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: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

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

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Q: The Bisection method is based on the principle that a continuous function which is positive at one…

A: Consider the provided question, We have find the value after third bisection process of the function…

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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Q: Find the area of a triangle bounded by the y axis, the line 2 f(x) = 6 - x, and the line…

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Q: Verify Mean Value Theorem for the function f(x) = x in interval [0, 9] %3D

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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: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, n]?

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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: 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: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

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: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

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Q: Determine if continuous f (x) = V4-x at x=0 %3D

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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…