x²+3x (t – 1)e' dt 2л — 4 - lim x→2

Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: In (**) 1+v1-x²' sech-1 x (A) O sech x

A:

Q: The area under the entire curve is given by 15 dx. We have 00 15x-3 dx lim 15x-3 dx - lim - 00 lim…

A: The area under the entire curve is given by  ∫1x15x3dx

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

A:

Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Find y double prime using implicit differentiation5x^3+4y^3=1

A: We have given,

Q: 1+3x – cosI 2.) lim tan x

A: limx->01+3x-cosxtanx When we plug in 0 for x then we get…

Q: In 1934, the Austrian biologist Ludwig von Bertalanffy derived andpublished the von Bertalanffy…

A:

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

Q: П 9. In(1+ kx) sin r x(ekz – x – 1) lim \k=2

A:

Q: Apply the secant method to solve f(x) = e** In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function.  f(x)=ex2lnx2-x=0. We have to solve by the secant method. Note…

Q: 2. Compute for a real root of sin va - x = 0 using three iterations of Fixed-Point Iteration Method…

A:

Q: dr (c) (d) lim sint dt

A: Given:

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

A:

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

A:

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: The approximation of the root x* of the function f(x) = -x + sin x - 1 accurate to within 10-³ using…

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

A:

Q: Find upper and lower bounds for

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

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Q: 8. Find the Laplacian of Ø = xy²z³

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Q: The approximation of the root x* of the function ƒ(x) = x* – 5x³ + 9x + 3 in the interval…

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Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

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Q: Question 1 00 is [ Select ] dx V2+5 The integral dx is [ Select ] The integral Vx2 + 5 [ Select ] dx…

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Q: 1. While using bisection method to find the solution of the equation f(x)=x*+3x-2=0 on interval [0,…

A: The given equation is x4+3x-2=0 on the interval [0,1] find f(0) f(0)=04+3(0)-2=-2 therefore f(0)=-2…

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

A: We will prove the following result.

Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

A:

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: 1 lim t→0+ (뉴 1 Vt2 +t,

A:

Q: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

A:

Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

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…

Q: 5.If the tangent 1ine to the functlen fx)= axt-6x at X=- has the equatfon. y= 3x+2then 6=?

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.