A ) is equal to the definite integral: - cot(- 3n The Riemann sum lim 3n cot(u) du | cot(u) du | cot(u) du cot(u) du

Q: Using the intermediate value theorem show that a  root exists between y= cos (Inx) on the open…

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Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

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Q: can i get step by step help please

A: Here the lower limit is v and upper limit is w.   The function f(x) = u

Q: Prove for a > 0:

A: Integration of the function helps to prove the required identity. A number can be written as the…

Q: 0 eg put (1) in f|L) = < ² cos(21), 3 siu (22), A 3√5 355 255 f(2)= < 3105 |24] 3sin (22) L

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Q: Prove the inequalities

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Q: Using the link between the Riemann sum and definite integral we se 70 n dx , lim n- co (n+1)2

A: Given: To explain the given statement as follows, Here, limn→∞ ∑i=1n 70 n(n + i)2

Q: Sin(3E)coSE- SinB LOSE Los t t

A: Consider the given limit: Here the objective is to evaluate the given limit.

Q: 812³ 72i a) The sum n4 n² i=1 Riemann sum of a function f(x) on an interval [0, 6], where b € N, b >…

A: Given that  is right Riemann sum of Now we rewrite given sum as follows: where Noted that Now

Q: The amplitude of f(8)= -0.9sing is: O 0.9 O -1 O -0.9 O 2n

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Q: What does the average velocity over the time interval [a, b) approach as we let b a. Mathematically…

A: Average velocity of a body is defined as the change in position or displacement (Δx) divided by time…

Q: J cos(9x) сos(x) dx

A: Use trigonometric identities and simplify the given expression than integrate it.

Q: The sine integral dt Si (): S* 3in (+) is important in electrical engineering. The inte grand f(+)=…

A: Given the sine integral Six=∫0xsinttdt ---1   Differentiating 1, we getf'x=sinxxDifferentiating…

Q: The Riemann sum lim Ecos() is equal to the definite integral: 3n 3n | cos(t) dt | cos(t) dt cos(t)…

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Q: e I 2 a) Find and classify the discontinuous point(s) of the function f. b) Is f differentiable at…

A: Given function is, f(x) =ex                  , x&lt;0x+2x               ,0≤x≤2sinx2-4x-2…

Q: Q Prove the following identities 1-sin (1) sec-tan ) 1 sin

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Q: Let f(z) = 1/z What is the image under f of the circle of radius 3, centered at 0? A circle of…

A: The answer is circle of radius 1/3

Q: what type of a calculus calculation is this?

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Q: Write the following limit as a definite integral on the interval [3, 8], where c, is any point in…

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Q: 6) a) Given z= f(x, y) =, evaluate f(x y) from (2,1) to the (1.95, 1.05) and calculate |Az|. b) Use…

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Q: Consider the function Where is f defined? Continuous? Differentiable? Twice-differentiable?

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: Ti The Riemann sum lim -csc(- -) is equal to the definite integral: 4n 4n n-00 Q10 csc(w) dw csc(w)…

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Q: x*+4x dx Riemaan Sum Note e ži=n4ti) 6.

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Q: Discuss the continuity of the following function: (2* (1– x), x 0 x = 0

A: Consider the given:

Q: Sa J (1+ In² sin x)5 “ cot x In sin x dx

A: Let the given integral be y - y = ∫cotx lnsinx1+ln2sinx5 dx           ..............(1)Let,u =…

Q: f(x) = e' and sketch the function b) expansion for even function f(x) = |cosx| and sketch the…

A: Fourier series

Q: Prove Jhab sinY Tim lim e-1 lim Sin y ニ ン と Siny S iny

A: Given,            limx→0sinxex-1=limx→0ex-1sinx=limx→0esinx-1xTo find : Prove the given limits.

Q: Apply Lagrange's theorem to exp(x + h), expanding about x = 0 to deduce that e = e¹ = 2² + R. Give…

A: We have to apply Lagrange's theorem to expx+h, expanding about x=0 to deduce that        e=e1=223+R…