x² – 7 x < 3 (1) Determine if g(x) = 1 x = 3 is continuous at a = 3. - 4 – Væ + 1 x > 3 Show why or why not.

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax – b -1 < x< 1, x 21 Continuous at x-0

A: from given function , the value of function in between 1 and -1 is ax-b. As x approaches to 0 the…

Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

A: Here I am attaching image so that you understand each and every step.

Q: 1. Examine the continuity and differential possibilities of function f (x)= |x² – 1| in x= 1.

A: Given To check for continuity at x=1 , we find the limit to the left and right of x=1

Q: 00 Suppose 0 < f(x)< g(x) and both are continuous on [a, o0). If | 9(x) dæ diverges, 00 | f(x) dx.…

A: We have to apply the comparison test

Q: -x² +1 Let f(x) be defined as f(x)={* - | 1–sin² x if x20 if x<0

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Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: 16 8 If f is continuous and f(x) dx = 10, find f(2x) dx.

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Q: 2. 지2 f f Š{(») = 6 , evaluate f(2sin6) Coso d@ is continuous and Sf(x)

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 1 x2 - х х x 2 Vx -2, Identify if the function g(x) is continuous/discontinuous at x=1. If…

A: Given: f(x)=1x2-x+1xx&lt;0-10≤x&lt;101≤x&lt;21x=2x-2x&gt;2 To determine: The given function is…

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: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

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Q: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

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Q: 1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2…

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Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

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: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

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Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: 4. Determine if g is differentiable at x = 0 if 2 cos-1 x, if -1<x < 0 g(x) = %3D if x 2 0. x + cos…

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Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 1. Use the properties of continuous functions to explain why f(x) =x cos(x) +1 is a continuous…

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Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

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Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

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Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

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: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

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Q: 4. `s.] Find the number a and b at which f is continuous everywhere? x² -1 if x 2

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

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: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

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