Question 2. Jse a Riemann sum with n=3 terms and the midpoint rule to approximate the value of sin(x2)dx. You lo not need to add the terms in the sum!

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: A rectangular beam is to be cut from a cylindrical log of diameter 20 in. d in. d in. (a) Show that…

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Q: Can you please answer this question and show all of the steps and say the correct letter

A: Consider the limit

Q: Define ro = 0 and xn+1 = In chis to Newton's method. tan(r,)-1 sec2(z,) What is lim, Pn in this…

A: In the given question we have to find the limit of the sequence xn as n→∞ where the recurrence…

Q: Question 4. (1) [x³² √x² + 4 dx. X3 sin (In x) X (ii) S -dx. Evaluate the integral: (iii) Choose a…

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Q: 3(1 — с cos x) sæ) 64. lim x→0

A: Just use L'Hospitals rule.

Q: Question 10 Given: y = xcos (x); Find y'". O(E) None of these Oy" xsin (x) + 2 cos(x) Oy" asin (x) -…

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Q: 3 7 cos z Evaluate the definite integral: dæ sin x 6.

A: Evaluate the Definite Integral : ∫π6π37cosxsinxdx

Q: Question 2 [17] 2.1 If f(x;y) = sin(xy) +x* In y, find f., at (0:4). 2.2 Let f(x; y) = arctan y 2+x?…

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Q: Find the length of the curve over the given interval. r = 6 – 6 sin(0) on the interval 0 < 0 s 2n

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Q: 3 1. Determine the order and the degree: sin x () - e* () = xy dx². a. Order – 2; Degree – 3 b.…

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Q: Question 4. Prove that the Riemann sum T(i + n) lim Cos n-00 n 2=1 can be written as a definite…

A: We prove that the Riemann sumlimn→∞ πn∑i=1ncosπi+nn  can be written asa definite integral ∫π2πfxdx

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: 2. Find the area outside the inner and inside outer loop of the limacon r = 4 sin 0 - 2 101

A: The equation for the Limacon is r=4sin θ -2 The graph given is

Q: 7. d. cos 0 cos 20 + sin 0 sin 20 = V3 over 0, 2t)

A: We know the sum identities: sin(a+b) = sina.cosb + cosa.sinb sin(a-b) = sina.cosb – cosa.sinb…

Q: 10 - f sin(82) arctan(sin 4x) da integralinin değeri aşağıdakilerden hangisidir? a) O T-2 b) - 8 8(T…

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Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

A:

Q: Question 2 d cos x Find dx In x A. X sin x x In x sin x+cos x x (In x) 1 COs X x In x sin x+cos x D.…

A: To find differentiation  ddxcosxlnx

Q: QUESTION 5 The Lower Riemann Sum utilises which function value on each subinterval? a. The square…

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Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: Question 9 Find n so that Tn (trapeziod rule with n subintervals) is guaranteed to approximate cos(3…

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Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

Q: In estimating cos(4x)dx using Trapezoidal and Simpson's rule with n - 10, we can estimate the error…

A: a = -1 b = 6 n = 10   h = (b-a)/10 = 0.7 h = 0.7   f(x) = cos(4x)   f'(x) = -4sin(4x) 0 = -4sin(4x)…

Q: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

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Q: Question 3. Let a € (0,1) and define f : T→R by 1 f(x) = sin(nx) na n=1 for all r E (-T, 7]. Prove…

A: We have

Q: Question 3 * Q3) Simplify (if necessary) then Compute: y¨+ 2y Where y(x) – |,raz (z'x t cosx*)|…

A: Given: To calculate  y'' + 2y' Here,  y(x) = ∂2∂x∂zz2x + coz x4 4 (cosh 2x - sinh 2x)16cos 2π xddx…

Q: Question 3 2 approximate '(x – 5)" dx using Riemann sum, the partition of 4 subintervals To X - each…

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Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

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Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

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Q: 10. Does there exist a harmonic function in z| < 1 taking the value 1 everywhere on |2| = 1? Is your…

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Q: A rectangular beam is to be cut from a cylindrical log of diameter 20 in. d in. d in. (a) Show that…

A: Here the rectangle beam is given, the diameter of the cylindrical log is 20 in.   part (a):   Now,…

Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: The sum of the series 1 + 2" + ... is n! ... 1! 3! A In 2 B e' cos 2 D sin 2 E nonexistent

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Q: Consider the DE, *x' + x -(sinl+)(cos(4) 1 et what method (s) can be used to solue thio DE ? Find…

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Q: A string is stretched and fastened to two points at a distance 'x' of 10 cm. Vibration is started…

A: The given problem is to show the displacement of initial shape of the string from the given…

Q: 2k sin(k/n), 212 lim is A-1 1. cos(1) +5/3. 2. cos(1) + 1/3. 3. cos(1) +2/3 4. cos(1)-1/3.

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Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: 1 The expression + sin 10 10 + .. + sin sin 10 + sin is a Riemann 10 sum approximation of which of…

A: We are given the expression               . It can be observed that x0=010, x1=110,..., x10=1010 as…

Q: QUESTION 5 10 If continuous and Jx)dx = 54, then which one of the following numbers can take at…

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Q: Question 4. Given the function v(2) = In(3 + sin(4z)) %3D and-the mesh = zo+ ih. where zo determine…

A: We are entitled to solve only one ques at a time and up to 3 sub-parts only. Given - Given the…

Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: sin 21 lim 2t

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Q: 1 3. a) Verify that sin x cos x = tan x--- π for the value x =-. 4 Ls Sin 4cos 4 2.s TanT/4-Y2 しS…

A: We can use the concept of trignometrical ratio in order to solve the given problem.

Q: Question 7: Use the trapezoidal rule with 6 intervals to evaluate f* 10 x7 dx ,giving the answer…

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Q: sin(k/n), lim is 1. cos(1) +5/3. 2. cos(1) + 1/3. 3. cos(1) +2/3 4. cos(1) - 1/3.

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Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: 3: Solve ODE Cist Order a. dY

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.