3) See the attached file -1 Vx-1 ,xs 2 ,x > 2 3-Let F(x)= is the function continuos at x=2 A) Discontinuous at x-2 B) continuous at x-2

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: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

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Q: 2. Consider the function / with domain (-2, o0): 3|2 – 1| 2 + 27 - 4 if – 2 <z<1 f(z) = if r = 1…

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Q: 8. If f is continuous and f(x) dx 10, find xf(x²) dr. %3D Give proper reasoning.

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Q: 3. If f is continuous and | f(x) dx = 10, find af(x*) dr. Give proper reasoning.

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Q: Suppose that f(x) is a continuous function on [a , b] and F(x)= | f(t) dt a Part 1 of the…

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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: Show that a function f : R? → R defined by S (7, y) = ! if (x, y) + (0,0) 0, if x = y = 0 is…

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Q: Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f" is continuous. Find the value of *…

A: Use the method for integration by parts to solve the integral.

Q: Is the following bounded or unbounded and why? f(x,y) = ln(x2 + y2)

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Q: If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [O,10]. True False

A: Given

Q: Find the Wronskian for the set of functions.{x, sin x, cos x}

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Q: If f(z) is continuous at z, then it must be differenttiable at z, ylgn O İhi O

A: If a function f(z) is continuous at z0 , then it may or may not be differentiable at z0. Hence, The…

Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: Suppose f is differentiable on some open interval containing e and f" (c) = 0 then (c, f(c)) is a…

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Q: Determine f(5) if f is a continuous function that satisfies +sin(a) f+sin(a) f(t)dt = 22² for all x.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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: 3. Use the e, d definition to show that f(x) = x² is uniformly continuous on A = [0,3]. %3D

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Q: Show that the functionf (x ,y)=xy³onD: x|<2, ]y|<oodoes not satisfies Lipschitz condition.

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Q: As the fun ction Leay) xy js Continuous I+ x*+y? e (-1, 2)

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Q: 2. Show that the function, defined by f(x) = is NOT uniformly continuous on its x2 %3D domain D(f) =…

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Q: lim, - f{x)= 0, then f(x)dx diverges Select one: O True False

A: When the limit exist or equal to 0 then the series is convergent otherwise divergent.

Q: Suppose that f is a continuous function satisfying stæ) = a f(t)dt + * So f(t)dt + a %3D for all a,…

A: Solve the function

Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

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Q: 3) See the attached file 3-Let F(x)= {* - 1 Vx -1 is the function continuos „x > 2 at x=2 OA)…

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the calue of c…

A: Given function is

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: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

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Q: 2. If f is continuous on [0, 1] such that x* f(x) dx=0, for n=0, 1, 2, 3,.. then show that f(x)3D0…

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Q: 1. Show (in terms of  ε - δ) that a function f : R3 → R defined by f(x; y; z) = (2x + 3y + 4z) is…

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Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

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Q: Suppose f is known to be differentiable and contains a local extremum at c, then which of the…

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Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: If f is continuous on [a, b] and cE[a, b], then f(x)dx does not exist. Select one: True False

A: Topic:- definite integration of continuous function

Q: Which of the following tatements is true about a mooth function f at (a, b) it ² (a, b) c, fax (a,…

A: f has relative maxima at (a, b) if D&gt;0, fxx(a,b)&lt;0 f has relative minima at (a, b) if D&gt;0,…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: Suppose f is differentiable on (a, b). If c E (a, b) and f' (c) = 0, thenf (c) is either the maximum…

A: Given f is differentiable on (a,b). and c lies in (a,b) such that f'(c)=0.

Q: (5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)|…

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Q: alue of c that makes the following function continuous: S 1+ cx if x 2.

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Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

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Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: 2. Suppose that f is a measurable function satisfying m{r ER: |f (x)| > n} ) < 1 nEN. n3 Is f…

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Q: 1. Use the e-ổ definition to prove that f(x) = x² is uniformly continuous on [a, 이.

A: