Given f is an even function integrable on the closed interval [-a, a] then | f(z) dæ is equal to a f(x) da -a a 2 f(2) dæ | f(2) dæ f(x) dæ f(x) da a

Q: Suppose a function a increases on [a, b}, a < xoS b, a is continuous at xo. Let f be a function…

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Q: consider the function f defined on [0,∞),f(x)=(x^r)sin(1/x),for x≠0 and f(x)=0 and for x=0, where r…

A: Solve the following

Q: 3. If f : R R is continuous at ro E R and f(ro) > 0, prove that there exists an interval containing…

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Q: Suppose f is integrable on [-b, b] and f is an odd function-that is, f(-t) = -f(t) for all tE(-b,…

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Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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Q: Consider the function of that is continuous on the interval [-5, 5] and for which ſo f(x) dx = 4.…

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Q: Suppose a function a increases on [a, b}, a < xo sb, a is continuous at xo. Let f be a function…

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Q: Let f and g be continuous on the closed interval (0, 5). Suppose that f(x)dx = A, f(x)dx =B, and…

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Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: Suppose f is continuous on the closed interval [-1,3]. If F is an antiderivative of f, which of the…

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Q: Show that the function f defined by (x, y) = (1, –1) f(x, y) = r? + y (x, y) # (1, –1) x + y is not…

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Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) &gt; 0.

Q: A function f is đefined on [0, 1] -as follows : f(x)= 1 when a? <x< (r=1, 2, 3, ...) f(0)=0, where a…

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Q: Let f be a function continuous on R and F(x) = x O f'(0) Of(0) ○ 2ƒ(0) O 0 *f(t)dt. Then F''(0) is…

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Q: (a) satisfies |f'(y) – f'(x)| < L\y – x| for some positive L and every x, y E R. Show that Let f: R…

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

Q: 5. Let f be a function continuous on R and F(x) = af f(t)dt. Then F"(0) is equal to 0 0 O f(0) ○…

A: Let f be a function continuous on R and Fx=x∫0xft dt. Then to determine the expression for F''0.

Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

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Q: Let f and g be continuous funCHons such that So f(x) dx =9,S f(x) dx = 5, and S g(x)dx= -7 what is…

A: Given, ∫06fxdx=9∫36fxdx=5∫30gxdx=-7

Q: Suppose f is a function such that f(n+1)(t) is continuous on an interval containing a and x. Then f)…

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Q: Suppose that |- f(x) is not constant. Il- f(x) is differentiable on 0, o0 II- S f(t)dt = (x +1)f(x)…

A: In the given question we have to choose a function which satisfies the given three condition in the…

Q: f(t) 1+ S. dt = %3D

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Q: f : R → R be defined by f(x) = x² + x. Pro nition, that f(x) is continuous at all a E R.

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that J f(x)dx = A, f(x)dx = B, and…

A: Given: ∫05f(x)dx=A∫03f(x)dx=B∫53g(x)dx=C…

Q: a) f(x)dx = 0 -- b) f?(x)dx = 2 | f²(x)dx -h

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Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

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Q: Let f ( x, y ) = ln ( ex * Y ) be a function. At which point the function is discontinuous? O a. (…

A: Given: f( x, y) = ln ( ex+y )     To determine: The point at which function is discontinuous.

Q: A function f is defined on [0, 1] as follows : 1 f(x)=, when 1 <x< a <*< =1, 2, 3, ..) (r=. f(0)=0,…

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Q: Let f be integrable on [-a,a]. If f is an even function, then f(x)dx is equal to a -a 2 f(x)dx

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Q: Σ sin k+1

A: to show that the given series ∑k=1∞1ksinxk+1 converges uniformly on R to a differentiable function f…

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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Q: Consider the function f defined on [0,∞) f(x) = xrsin(1/x), for x≠0 and f(x) = 0, for x=0 where r >…

A: Given: f(x)=xr sin1x,   x≠00         ;     x=0     a) f is continuous on [0,∞) f is continuous if…

Q: Let f be the function defined by f (x) = r ln I for ¤ > 0. On what open interval is f decreasing? A…

A: Explanation of the answer is as follows

Q: 4 Suppose that f is continuous function such that |F( x) # x and 4 [(4x)dx = 3. Then fxf(4x² )dx =?…

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Q: Define f: Z x Z→ Z x Z by f((m, n)) = (3, 2n). Let A = {(n, 0): n ∈Z}. Fina f(A).

A: EXPLANATION : Given function  f:ℤ×ℤ→ℤ×ℤ defined by fm,n=(3,2n). given set A={(n,0):n∈ℤ}. putting the…

Q: If f is continuous on [a,b], then the function g defined by g (x) = S f (t) dt, a < x < b is…

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Q: Suppose f is continuous on the closed interval [- 1,3]. If Fis an antiderivative of f , which of the…

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Q: ind the absolute maximum and minimum values of f on the given interval. a) f(x) = on [0, 2] g2+1 on…

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Q: Suppose f is a differentiable function with f(7)=1 and f '(1)=- Let y= f(x)·tan x+e* •cos x . Then…

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which f f(x)dx = 4.…

A: We need to evaluate integral.

Q: In r Consider the function F(x)= dt (for r>0). What is F'(x)? %3D F'(x) = e In a O F'(2): In r In x…

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Q: Suppose a function a increases on [a, b}, a <xo Sb, a is continuous at xo. Let f be a function…

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Q: Suppose that the function f is continuous everywhere. Suppose that F is any antiderivative of f, and…

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Q: Let f(x) be continuous on [0, oo) and twice differentiable on (0, co). If f'(x) > 0 and f"(x) 1,…

A: Let f(x) be a continuous function on [0,∞) and differentiable at 0,∞. The given double derivative…

Q: Suppose that f:I → R and g: I → R are differentiable at c E I. Then, a) If k E R, then the function…

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Q: 3. Let f(r) = r sin() if z #0, and f(0) = 0. Show that f is continuous at r= 0 by using e- d…

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Q: if (x, y) # (0,0) (1 if (x,y) (0,0) x+y (a) Prove that the function f(x, y) =2x+y is not continuous…

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Q: The Fundamental Theorem of Calculus (Part 1) states that if f(x) is a continuous function on an…

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