Question 4 Let f(x) be a function and be R. f is continuous at x = b if and only if : 4.1 4.2 4.3

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A: If a function is differentiable at 'a' then f is continuous at 'a' but converse not true.

Q: Question 10 If f is differentiable on (-oo, o0) and f(-1) = f(1) , then there is a number c such…

A: The answer is given below:

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Q: Question.1 Let f: [a, b] → R be a continuous function. Prove that fE R. Is the converse true? Why?

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Q: 5. Consider the function below. Is g continuous on (0,1]? on (4,1)? Why or why not? if x 4.

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Q: Question 4 If f is continuous on [a,b], then T) True F False [xf(x)dx= x₁ b a f(x) dx

A: Given query is to find the statement is true or false.

Q: 2. Which of the following functions satisfy the hypothesis of Rolle's Theorem on the interval [0,2]?…

A: For fulfilling Rolles theorem there are three conditions to satisfy so I'm providing hand written…

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Q: Question 7 Let f : R - R be a continuous function which does not take on any of its values twice. Is…

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Q: 10, Let f be the function defined by the following. sin x, x<0 x. Osx<1 S(x)={ 2-x, x-3, x22 For…

A: Given: the function f defined by the following             fx=sin…

Q: QUESTION 11 Let f:X Y be a continuous function. If X is disconnected then so is f(X). O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given f∈S(R) is an even function.

Q: Question 9 A Let f be the function defined by f (2) = r In z for z>0. On what open interval is f…

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Q: . Show wheth er the following function is continuous at x = 0.

A: Givenf(x)=4x-9 if x&gt;-33x+6 if x≤-3

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A: When curve below x axis then integral is always give negative values for that region

Q: Question 13 Suppose f: RR is continuous, and let a, b, E R. For which choices of a,b is the function…

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Q: QUESTION 11 Let f:X-Y be a continuous function. If X is disconnected then so is f(X). O True O False

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Q: Question 6. For what value of b is x, x -2 continuous at every x?

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Q: If a function f: D R is differentiable at a point (a, b)ED, then f is continuous at (a, b);

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Q: Question 2: Tutorial 10 x² and g(x) (b) If f(x) x³ with x € [1,1], find the c € (-1, 1) by using…

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Q: Let f(x)=x in(x). Find the interval on whichf is increasing. (a) (0, e- 2] (b) (0, o) (c) [e- 2, 0)…

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Q: Question No: 4 Discuss the continuity of the following functions if not then give reason: • f(x) =…

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Q: Question 14 Which of the following statement (s) below is(are) always true? I. If f(a) exists, then…

A: We have to check

Q: s-8 Define f(2) in a way that extends f(s) = to be continuous at s = 2. 2 - 4

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Q: 5 Question .4 Verify Mean Value Theorem for the function f(x) Vx in interval [0,9] Abc أدخل إجابتك

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Q: 73. Let x + 2 if x 1 Find the value of k that will make f continuous on (- ∞, ∞). Answer J

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Q: Suppose that we know that the function f(x) is differentiable at = a, then what must always be true?…

A: We have to choose correct option

Q: Question #2: Suppose f (0) = 0 and f"(x) > 0 for all x > 0. %3D Show that g(x) = is increasing.…

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Q: Question 3 In(x²) + 4 2 Consider the continuous function h with h'(x) 3.1 Find and represent the…

A: 3.1 The function can be obtained using the fundamental theorem of Calculus: h(x)=∫h'(x) dx…

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Q: For what value of the constant c is the function f continuous on (- o0, 0) where S (1)² – c if y 2

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Q: Question 2 ( Consider 2x – a2; 0 4 2 - x; x - 4; %3D T; which statement below is correct regarding…

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Q: 5. Consider the function below. Is g continuous on (0,1]? on (4,1)? Why or why not? if x 4.

A: Given, g(x)=xif x≤03if 0&lt;x≤13-x2if 1&lt;x≤4x-3if x&gt;4

Q: Consider the function below. Is g continuous on (0,1]? on (1,4]? why or why not? if æ 4.

A: Explanation of the answer is as follows

Q: Question No 3: For what value of 'a' is f(x): (2-x², x<2 lax + 1, x2 2 f(x) = continuous at every x?

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Q: Question 6. defined function is continuous everywhere: Determine for which values of a the following…

A: To finds values of a we will use the basic definition of continuity

Q: QUESTION 3 Suppose f: R→ R satisfies |f(x)| = |x| for all X. Which of the following is true? Of must…

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Q: Question 15 If f and g are continuous on a, b, then 9. f(x)g(x) dx = (/ f(x) dx (7 9(z) dz a. O True…

A: Definite integrals can be computed using the fundamental theorem of calculus. Fundamental theorem of…

Q: Question.2 Let f: [0,2] → R be a function f (x) = {x, ifx 1 Show that f is R – integrable. |

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Q: QUESTION 1 Suppose that f:A → PR and CEA, To say that f is continuous at C is equivalent to saying…

A: To state true or false.

Q: QUESTION 4 ху? Let f(x) = { Jx²+y? if (x.y) # (0,0) if (x,y)=(0,0) lim f(x.y). (x.y) → (0,0) a)…

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Q: If f(x) is a function and f'(a) exists, then f(x) is continuous at a: a. Never b. Sometimes (it…

A: Let f(x) be a function and f'(a) exists That is f is differetiable at x=a

Q: Question 2 Iff and g are continuous on [a,b], then t True B) False in √ [f(x)g(x)]dx = {√°f(x)dx)(√°…

A: Given that f and g are continuous function on [a,b].

Q: Question 8 x² if x2

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Q: Question 2 find the derivative f'(x) using the limit definition, if it is not, show why not. For…

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Q: A) Find the values of a and b that make f (x) continuous for all real x. be + a+1, f(x) = { ax? +…

A: Please see the explanation below

Q: Question 17 Indicate if the following statement is TRUE or FALSE. Briefly justify your response with…

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Q: f : [a, b] – is exactly two-to-one (Vy E R, ƒ¯1) = Ø or ƒ¯'(y) is a 2 12) Suppose point set). a)…

A: We need to produce example of two to one map and need to show that no such function can be…