f(x)={x^2−9x≤c, 2x−10 x>c } i

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

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

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

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: Express the limit as a definite integral on the given interval. lim (5(x)3 – 7x]Ax, [2, 6] n- 00 = 1…

A: Consider the given limit and interval. limn→∞ ∑i=1n5xi*3−7xi*Δx and interval=2,6 Now, go through the…

Q: Express the limit as a definite integral on the given interval. lim [9(x;")³ – 4x;]Ax, [2, 8] i = 1…

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Q: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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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: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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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: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

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Q: What is the total area between f(x)=2x−7 and the x-axis over the interval [0,5]?

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Q: Q2. Give a counterexample about a bounded function that is not Riemann integrable.

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Q: Express the limit as a definite integral.

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Q: What is the local linearization of f(x) = arcsin(1+4x) near x = −1/4   arcsin(1+4x) ≈

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Q: Express the limit as a definite integral on the given interval. [5(x;)3 - 3x;]Ax, [2, 6] n- 00 i = 1…

A: see below the answer

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

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Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: What is the Extreme Value Theorem for continuous functions?

A: Extreme Value Theorem According to this theorem, if a function y=fx is continuous in a given…

Q: Find the higher-order deriv f"(x) =6Vx – 4 f(5)(x) =

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Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: Express the limit as a definite integral on the given interval. lim n - 00 -Дх, [1,5] (x*)2 + 6 dx

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find the absolute extrema of the function on the closed interval. TEX y = tan 16 ), [0, 4] minimum…

A: Given that, The function is y=tanπx16 on the closed interval [0, 4]. To find absolute extrema:…

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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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: What is the absoluite extrema of the function h in interval [0, π]. Calculate and state the…

A: Exponential and sin, cos are always continuous

Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

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: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x – 2…

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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: 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: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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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: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

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Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: Express the limit as a definite integral on the given interval. cos X Дх, [Зя, бя] lim 6x X dx 3x

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Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

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: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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