Iff is bounded and integrable in the interval [a, b], f(x) cos nx dx=0. show that lim

Q: By considering different paths of approach, show that the limit xY COS Y lim does not exist.…

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Q: Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

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Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: 2. Show that f(r) = sin r is uniformly continuous on (0, 00). %3D

A: 2. We need to prove that sinx is uniformly continuous on 0,∞. Definition of uniformly continuous…

Q: Express the limit as a definite integral on the given interval. in lim [5(x,")3 – 2x,*]Ax, [2, 7] i…

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: Rewrite , 15 dx as a limit and then show that the integral diverges.

A: Given

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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Q: Compute the limit as x approaches infinity of x^e-x

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Q: If f is continuous everywhere except at x = 2, then f(x +1) dx is not integrable. True False

A: To check whether the given statement is True or False."If f is continuous everywhere except at x=2,…

Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

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Q: Show that f(x) = In x is not uniformly continuous on (0,2)

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Q: evaluate the limit  limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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Q: Evaluate the limitlimx→0+x sin(x) + x^2/ x^2

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Q: Express the limit as a definite integral on the given interval. lim -Дх, [1, 4] (x;")² + 9 i = 1 dx

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Q: Express the limit as a definite integral. n lim > 2 cAx, where P is a partition of [3,8] n00ks1

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Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: Determine the following limits analytically.

A: Given: The limit expression limx→π21-sin3xcos2x, To find: The value of given expression.

Q: Use L'Hospital's rule to evaluate the limit sin(3t) dt lim X-0 x2 O O

A: We have, limx→0∫0xsin3tdtx2 On solving further the integral part, we get the result as…

Q: 3) Examine the limit of 1 (x² +y²).sin- x*+ (x, y) (0,0) f(x, y) = (0, (x, y)=(0,0)

A: Solution:Givenf(x,y)=x2+y2 sin 1x2+y2To Eamine the limit of a functionFormula:limx→0 sin xx=1

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Find a value of k making h(x) continuous on [0, 5]. kx 0 < x < 2 x + 1, 2<x < 5 h(x) =

A: The given function is hx=ekxif 0≤x&lt;2x+1if 2≤x≤5. The function is continuums. That is,…

Q: Express the limit as a definite integral. 5 lim 2 cAxK, where P is a partition of [2,11] ||P|→0k=1

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Q: Determine the largest interval over which the fu Vx+2 is continuous.

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Q: Is g(x) = ln( x2+2 ) uniformly continuous on the interval (−∞,∞)?

A: given function is                                                        g(x)=lnx2+2 log is defined…

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

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Q: 2. Show that the function f(x) = cos x is uniformly continuous on

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Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: Express the limit lim,, +00 Ei-1 8i2 as a definite integral.

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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: Let fn f, where if 0<<! Sn(x) ={ S 2-a if 0<x<1 and f(x) if a = 0 Then lim sup fn (x) – ƒ (x)| =

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Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: Prove: the limit as x approaches 0 1-cos(x)/x=0

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Q: If f is bounded and integrable in the interval [a, b], (x) cos nx dx3D0. show that lim

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Q: The limit lim Sz; sin(x;)Az i=1 can be expressed as a definite integral on the interval [0, 7] of…

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Q: Express the limit as a definite integral on the given interval. lim S 19(x/)³ – 8x;]Ax, [2, 5] 1

A: The definition of definite integral is, ∫abf(x) dx = limn→∞ ∑i=1n f(xi*)△x   in the interval a, b…

Q: If |fn(x) – fn(y)l 0 and all x, y in a compact interval, show that {fn} is uniformly…

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(9x) lim x →0

A: Please refer the attached image for complete solution. THANK YOU.

Q: If f is integrable on [a,b], show by example that F (t) = | f (x) dx is continuous but need not to…

A: We need to show by an example that if f is integrable on [a, b], then F(t) (as defined in the…

Q: Find the following limits proving whether they exist or do not exist 5y¹ cos²x x² + y² C) D) lim…

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Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: Let f (x) = xex . Use the limit definition to compute f ,(0), and find the equation of the tangent…

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Q: 1. Estimate the limit of the signum function s(x) as x approaches zero from the right. (-1, x0

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Q: Find the limit sin(3x)cos(4x) lim→0 x+xcos(5x)

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Q: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

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Q: is continuous lim x f(x) = 0 = f is continuous in 0.

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