10. If functions fix) and gx) are continuous everywhere, then A. (f/g) (x) is also continuous everywhere B. (f/g(x) is also continuous everywhere except at the zeroes of g(x) C. more information is needed to answer this question D. the question is insufficient

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

A:

Q: Suppose that f: [0,1]–R is a function satisfying the conclusions of the intermediate value theorem.…

A:

Q: 3. Show that the functionf on [-1,1] defined as if f (r) = 1+e if x = 0 is discontinuous at x = = 0.…

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Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

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Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

A:

Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

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Q: Discuss the following theorem: If a function is differentiable at, then is continuous at. Provide…

A: Assume the point as x = c. Thus, if a function is differentiable at c , then is continues at c. Let…

Q: 18. Suppose that f is a differentiable function such that f(g(x))= x, and f'(x)= |3D 1 1+(f(x))².…

A:

Q: 1. What is the definition of what it means for f(x) to be continuous at x = a? Discuss the ways that…

A: In this question, we need to define the meaning of f(x) to be continuous at x=a and different ways…

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)>0 then function increasing when f'(x)<0 then function decreasing

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: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

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Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: 2. Consider the function if x = in lowest terms q > 0, p, q € Q; f(x) = O if x e Q°,x = 0 Question:…

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Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: 35. Given that f(z) is a continuous even function, then A 0 B D

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Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: Suppose that a function h satisfies −x^2 ≤ h(x) ≤ x^2 for all x. Prove that h is differentiable at x…

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Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: Can Rolle's Theorem be applied to f(x) = 1/(1-x) on interval [0,3]? If yes, what is c in (0,3) such…

A: here we can't apply the rolles Theorem

Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

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Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: 16.C. If f is defined and continuous on R? to R and if f(xo) > 0, then is f positive on some…

A: Consider the provided question,   We need to show that, f is strictly positive on some neighborhood…

Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

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

A:

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

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…

A:

Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: 2. Show by definition that the function f : R R, f(x) = ||, is continuous on R. Hint: you may need…

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Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: (1- a? f(x) = 1– x² if x E Q, if r ¢ Q. %3D p at which f is continuous. Prove your conclusion.

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Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…

A: Let f be any function that is not differentiable  at the point a and define as: gx=-fx for all real…

Q: Let f(z) be a real valued function defined for satisfying f(1) = 1 and f'(2) = then lim f(z) =)…

A: Given function is, f'x=1x2+fx2 The above equation f'x is always positive which means fx  is always…

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: If a function is real and continuous in the region from a to b and f(a) and f(b) and if both have…

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Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.

Q: If f:R → R is continuous at both 2 and 4, then f must be continuous at some c E (2,4). Select one:…

A: Consider the function f:R→R, that is continuous at both the points 2 and 4. Let there be a point c…

Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.