If continuous or f differentiable is [ Select] on [a , b] then the [Select ] integral of definite or f indefinite on [a , b] is equal to G(b)–G(a) where G is [ Select] of f the derivative or an antiderivative or the definite integral

Q: True or false: If f has a derivative at x = 2, then f is continuous at x = 2.

A: To determine whether the following statement is True or False.If has a derivative at , then  is…

Q: The function f (x) called invariant under differentiation operator function (IUDO. function) if:…

A: The given functions are ux=-2coshxvx=-sinhx+coshx Now firstly we will find the derivatives of u(x)…

Q: Evaluate the definite integral by the limit definition

A: Here,

Q: 1. T ... Šketch a graph of a continuous and differentiable function, f, with domain (-o, c0), that…

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Q: Find the domain and the derivative of the function f (x) = In x + V x² -25 Enter DNE in any empty…

A: The graph is shown below:

Q: If f is an entire functions then h(z) = e² f(1/2²) is analytic on C\ {0}, and its derivative h'(2) =…

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Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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Q: Suppose f" () > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: Step 1: Let write the given .We are given that f"(x)>0 on some interval (a,b). Step 2: Let write…

Q: x-1' Find the value of the constant A for which the follo

A: Find the value of A

Q: Determine whether the statement is true or false. '8 If f'is continuous on [7, 8], then f '(v) dv =…

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Q: Is a function Continuous ?why? integrable anod

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Q: Let / be a twice differentiable function. One can show that e* (exf)" = af" + bf' + c, where a, b, c…

A: NOTE: Refresh your page if you can't see any equations. . use the product rule for the derivative

Q: Let (f) be a continuous function with the definition area a closed interval. Show that if (f) has an…

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Q: Let f(x) — sin(nx) n³ n=1 Show that f is differentiable on R and that f' is continuous on R.

A: Within its interval of convergence, the derivative of a power series is the sum of derivatives of…

Q: Assume that the functions ?,?,ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c,…

A: given: ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c, h′(c)=d, f(a)=e, g(e)=ℓ,…

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Which of the following will make the function f(x) = VE-2 discontinuous? 215 O a. 2 and 5 O b. 3 and…

A: Note:- according to the company policy we can attempt ?️ only one question so please upload the next…

Q: Find the antiderivative of the improper interval xe-x^2 from negative infinity to positive infinity

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Q: Make sure you do your best to answer all three parts. Suppose f(x) and F(x) are continuous functions…

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Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

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Q: TRUE OR FALSE. a) f is increasing on (-∞, -3). (b) f is differentiable on x = -3. (c) f" is…

A: A differentiable one-real-variable function is one that has a derivative at each point in its…

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) .