2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

Q: dy +y = zy dr

A: Given equation is: xdydx+y=xy3

Q: 1.4 Calculate an approximate value of the integral S (sinx – Inx + e*) dx by - 0.2 dividing the…

A:

Q: 22. How large should n be to guarantee that the Simpson's Rule approximation to e dx is accurate to…

A:

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

A:

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

A:

Q: Find the following indefinite integral. (5 -0.25x Jox=D -0.25x +3e d%xD (Type an exact answer in…

A:

Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

A:

Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

A:

Q: 2) Find L{te"sin5t} using two methods. ans: (s+2)2+25

A:

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

A:

Q: If we let u = cos t, then the integral [(sint). In (cost) dt can be expressed as - [In(u) du 0…

A: An integral is given. We have to write the substitution form of the integration in terms of the…

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

A:

Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

A:

Q: Find cosh a In(sinh r)dr.

A:

Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

A:

Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

A:

Q: / (3cosh m 2 cosh m sinh mdm +e°

A:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: 2) Give a big-Oh estimate, O(x³), for the function f(x) = (1 + 2x + 2cosx + 2r*)(log x² + 3lx| + sin…

A: 2 Given function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx. We have to estimate Ox3 and determine the…

Q: dy dr

A:

Q: -aluate the following integral cln 2 cosh x UTM =dx. sinh? x + 4 sinh x + 2

A:

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

A:

Q: If the definite integral of (1 + sin y)dy with lower limit equal to zero is π+2, its upper limit is…

A:

Q: Evaluate the given integral. ∫ (e2x cos x -2e2x sin x)dx.

A:

Q: Find cosh r In(sinh a)dr.

A:

Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

A: Simpson's rule error bound    Es≤kb-a5180n4 , where f4(x)≤k where ∣E​S​​∣  this e absolute values of…

Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

A: We need to find how large should n be.

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

A:

Q: In (6x) to x if y = sin (5e') dt.

A:

Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

A:

Q: 5 Only one of these calculations is correct to evaluate the definite integral 7x In(x) dx Using the…

A:

Q: Consider the following. 6. 13 In(x) dx Let u = In(x). Find du. %3D du = dx Indicate how the limits…

A: Let us consider the integral, ∫1913 lnxxdx

Q: Find the indefinite integral. ∫e4x cos 2x dx

A: Here given integration as I=∫e2xcos 2x dx

Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

Q: Evaluate the following integral cln 2 cosh x dx. sinh² 0. x + 4 sinh x + 2

A:

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: (4z + 5)² tan zy= + dr Cos z

A:

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

A:

Q: 3. Find the indefinite integral. S (3e* + +x³ + 3) dx

A:

Q: 2. Find the following indefinite integrals. 3 + yx)dx

A: Since you have asked  multiple questions in single request  so  will be answering only first…

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

A:

Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....

Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.