Г(п + 1) (т + 1)"+1 I(n).k>0] 1 3. Show that, / (In-)" dx [Hint:/ -kx n-1 e kn

Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

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

A: We know that, ∫lnxdx=xlnx-x+C…

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: verify the statement by showing that the derivative of the rightside equals the integrand on the…

A: Given statement :

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

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Q: find the derivative.

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: We write the expression using exponent and then integrate C=integrating constant

Q: 2 9) -sinh? -cosh -dz

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Jse differentials to approximate 47. (Express as a rational number.)

A:

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Find dy of Using first principles

A:

Q: Vz²+1 ev° dy In a

A:

Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

A:

Q: Approximate using differential √627( answer in fractional form)

A: Let y=f(x)=x4where x=625 & ∆x=2

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: 4) What integrals lead naturally to inverse hyperbolic functions?

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Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: complete solution

A:

Q: sec Vn du in

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Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

A:

Q: Find 2. dy of 2.

A:

Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

Q: Use a linear approximation (or differentials) to estimate the given number. 99.8

A: To find √99.8

Q: A particle is moving with S. H. M. while making an excursion from one point of rest to another, its…

A:

Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Integrate by Gaussian quadrature (n=3). dx Ji 1+x*

A:

Q: Use the hyperbolic identity cosh(2x)= 2 cosh2 (x)-1 to solve 4 cosh(2x)– 22 cosh(x)+ 19 = 0 .

A:

Q: Use differentials to approximate √16.5.

A: Given:

Q: у %3DIn(In sec x)

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: The value that will satisfy potential function p is

A:

Q: Use a linear approximation (or differentials) to estimate the number V100.5

A: To find 100.5Let y=xLet x=100 and ∆x=0.5⇒y=100y=10Differentiate…

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

A:

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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Q: Use a linear approximation (or differentials) to estimate v3.99 to 5 decimal places. Be sure to show…

A: