1 f(1) =1-2 t- 2

Q: Consider the function if a<0 2 + I if0<I < c, g(x) = if a c where c is a positive constant. Show…

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Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Given: f(x) = ln (9 - x 2) To determine: The domain of the function and prove that it is continuous…

Q: The following statement is false, explain why. The function g(x) = x^2 on the interval [-1,1] has…

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Q: 34) If f is an even function that is continuous on [-1,3] and if f f(t)dt f₁f(t)dt = 8, then f…

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Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

A: Given the function is We have to sketch the graph of the function and also check whether it is…

Q: Find the value of the constant k so that f(x) is continuous for all real values of x where f(x) is…

A: Solution

Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

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Q: 1- Vx – 2 f (x) = x + 3, x – 3 k x = 3

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Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2&amp; -2…

Q: c =

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Q: 3. Define the function sin(2x – 2) x 3 3' - Determine if f is continuous at x = 1 and x = 3. If…

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Q: sinkx) x 0

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Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: Use Theorem 9.2.1 to show that T is not continuous at 0, no matter what value is chosen for b.

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Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: Assume that the function f is such that f(3) = 1, ſ f(x) dx = 5, and f'(x) is continuous on [0, 3].…

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: The graph of f(x) has a corner at (a, 1(a)) if f(x) is continuous at 'a and left-hand derivatives at…

A: In this question we will use basic of calculus i.e concept of continuity and differentability. We…

Q: Determine if the given function is continuous at the indicated number x = c. |x-3| if x#3 4. j(x) =…

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Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) &gt;0. Does f have a local…

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Q: Consider the piecewise-defined function Vx+ 1, x> 3; f(x) = { 2b, X = 3; x < 3. %3D ax + b, Supposef…

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Q: Suppose a function f is continuous on [0, 1], except at a = 0.25, and that f(0) = 1 and f(1) = 3. Is…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Consider the following piecewise defined function: sin(ax) -1 < x < 0 4x f(x) = a2 –(b+1)x+b x²+x-2…

A: Given function is f(x)=sin(ax)4x,-1≤x&lt;0x2-(b+1)x+bx2+x-2,0≤x&lt;1x2-1+a ,1≤x≤2…

Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

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Q: Suppose that f : R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the 8–neighborhood…

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Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Consider the function f with domain (-2, ): 3|x2 – 1| 2x2 + 2x – 4 if – 2< x < 1 f (x) = 3 if x = 1…

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Q: make a sketch of the given function on the interval[0,∞).

A: Given: To Plot:

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: . Find a value of k so that the following function is continuous at x = 1. f(x)%3D x<1 x-1 2kx, x21

A: Given: The given function                                             To find: The value of k, such…

Q: and if the function is differentiable at x

A: The Given function is f(x)=x+33  ,  a=-3

Q: |Consider the function f with domain (-2, 0): 3|1² – 1| 21² + 2r – 4 if – 2<1<1 f(z) = if x = 1 3 if…

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Q: Find the value/s of a such that the function f is continuous everywhere.

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Q: Let f be a function that is continuous on the closed interval [1, 5] with f ( 1) = 10 and f (5) =…

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

A: The given functiong(x)=7x+2-6x+4x-2,if x≥-27 and x≠2k,if x=2

Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

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Q: (2) Find an example of a function f : [0,1] → R such that f is not continuous, but that f satisfies…

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Q: Consider the function f with domain (-2, 0): 3|a2 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: 7. Find the intervals on which the function is continuous, J (X) = +3)2+6

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Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

Q: 2. h(x) = at x = 1 x+1 %3D x2-1

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Q: Suppose that f is a continuous, strictly increasing function on [0, 1] and that the •1 range of f is…

A: Here given function is continuous and strictly increasing function on [0,1]