2x Write the integral e eat d x as the limit of Riemann sums using the right endpoint rule. That is, S e2ª dæ = lim (E- lim (E-1 -). - n→x

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

A: We have to find the value of delta(d) in terms of x0 and e while evaluating the limit at x := x0 for…

Q: One of the following ODE is a linear DE of second order O x³y"-3y'=e*+xy O None of these O…

A: We are given some ODE and out of which we have to identify which ODE is linear DE of second order.…

Q: Let F(n) = EdP|n®p(d). Show that if F(1) n = pi" ..P"n=p, then F(n) = II" 1 P" 1 and that if n > 1…

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Q: 5. Evaluate the definite integral (2x-3)dx as limits of Riemann sums (Use equal partitions an and…

A: To Determine :-  The definite integral  ∫13  2x2 - 3  dx  as limits of Reimann sums.

Q: Q1:Proof the following Limits : (In n` п b. En=2 c. Σ-1 ! e-n а. С. 2n-1 z=D1

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Q: Write the following limit as a definite integral on the interval [5, 11], where c; is any point in…

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Q: Compute lim n · (Vỹ – 1). | n→∞

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Q: D) How an un 04 A ) Use sandwich theorm to find the limit of the function g(x) as x approach zero.…

A: By the Sandwich theorem , if f(x), g(x) and h(x) be three function such that f(x) <g(x) <h(x)…

Q: 1.3 Let fn: (-3, 3] R be defined by fa(r) Find the pointwise limit of fa(x). %3D

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Q: Find lim t→ 1 1 - cos2 Int 0(0.20 를 를) 0 O t ./t+7, t-1 t2 − 1

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Q: Let f be a continuous function with domain R. Compute the limit (z- t) f(t) lim dt.

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Q: 3. Let fn(x) = ¹+cos(nx), x € R. Find f(x) so that fn → ƒ pointwise on R, then check whether fn → f…

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Q: f(x) = x² + 1 4 calculate 19 Så lcxjdx 6 3 jeza lim 87x +1) using using deli = lim [ {Rexi)ox] 946…

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Q: ulsu (un (a) u

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Q: 99. Show that 00 cos x dx is absolutely convergent.

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Q: Write the following limit as a definite integral: limn→∞ ½ / Σ²-1 ( ²1 )º n j=1 of th x6 dx f²x5 dx…

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Q: 21. Please express sin(t³) dx as a limit of right regular Riemann sums. a. Ax= b. Xk =

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Q: One of the following ODE is a linear DE of fourth order Oxy-3y'=e*+xy² O None of these O xy"-3y'+y…

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Q: Let fn(x) = tan" x on [–1/4, /4]. Find the pointwise limit f(x) as n → ∞, and etermine whether fn →…

A: Given that The pointwise limit is,

Q: If f is continuous on [0, π], use the substitution u = π-x to show that π [" xf(sin(x)) dx =…

A: To prove

Q: If f is continuous on [0, π], use the substitution u = -x to show that -76 2 ["xf(s xf(sin(x)) dx =…

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Q: el 29-38 Determine the set of points at which the function is continuous. 29. F(x, y) = xy 1 + e*- 1…

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Q: y' + y" = 2x²y 10y' - y = ex 2 tanh(y)y′ +2xy+3=0 y” = tanh(y/x)

A: To define whether each of the following ODEs are 1st-order linear, 1st-order non linear,2nd-order…

Q: Express each limit as a definite integral: n lim n→∞, i=1 πί sin + (4 2n. 2 5k -1+ 5k lim 2 п k=1

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Q: Let fe C[0, 1]. Show that E lim n→∞ of |f(x)|¹dx n max |f(x)\. x= [0,1]

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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