I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh x

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

A:

Q: Compute the following derivative: 1 -3/x dx sin(x)

A:

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: Evaluate the integral (exact value). e2X sin(8x) dx =

A: We have to find the integral.

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 )

A:

Q: sinh x dx 1+ cosh x

A:

Q: If f(x) = e*sinh x, what is f'(x)? e*(cosh x- sinh x) O Option 1 Option 2 e*(sinh x - cosh x) 2e2x…

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Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

A:

Q: Compute the derivative cos(sin(e7))

A: cos(sin(e7)) We need to find the derivative of the given function.

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

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Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: In the given question, verify the identity:- sinh(x + y) = sinh x cosh y + cosh x sinh y

A: Consider the provided identity, sinhx+y=sinhx coshy+coshx sinhy Verify the provided identity.…

Q: Find y" by implicit differentiation sin y + cos x = 1

A:

Q: sin(20nnt) AS(t)ln:odd = Ln=1 %3D

A: The Given problem is:…

Q: In the given question, verify the identity:- cosh x - sinh x =- e-x

A: As we know that the hyperbolic function of the inverse trigonometric identity is given by as…

Q: Obtain the derivative formulas for csch x, sech x, and coth x from the derivative formulas for sinh…

A: Given functions are sinhx,coshx,tanhx.

Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: sinh(In In a)da is equal to xlnx

A: To find:∫sinhlnlnxxlnx dx

Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: y = e*In(sinh x)

A: See the details solution in below

Q: Differentiate the following using chain rule Y = In (cot 3x – 2) Y = log cos? 3x

A: We need to find the derivative of Y=ln cot 3x-2 and Y=log cos23x. First problem: Now,…

Q: y= Arccos(e2x)

A: Given: y=arccose2x To Find: The second derivative y'' of the given function and to simplify the…

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

Q: Evaluate the integral.

A:

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

A:

Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

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Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

Q: Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

A: Hyperbolic functions: These functions are defined as the algebraic expressions of the exponential…

Q: Find y' for the following xy = sinhx+coshy

A:

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: y= Arccos(e2x) х-1 y = log Vx+1

A: We know that,  ddxcos-1(x)=-11-x2ddxlogx=1x Along with these results we use the chain rule for…

Q: cosh(2x) = cosh?(x) + sinh² (x).

A:

Q: 3. Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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Q: sinh x 1+ cosh x

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: Find the indefinite integral. ∫e−3x sin 5x dx

A: ∫e-3x sin5x dx

Q: y = [cosh(ln x) + sinh(ln x)] 2

A:

Q: Solve for the second derivative(y") of the following and simplify the final results. Show complete…

A: Given. ⇒4lntan-1x=1-y⇒y=1-4lntan-1x Taking derivative with respect to x, we get…

Q: Differentiate each of the following functions with respect to x. 1. y = In cosh2x 2. y = e" sinh x…

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Q: Find the indefinite integral. sinh(2 – 9x) dx

A:

Q: arc sin z = -i log(iz + V1- 22).

A:

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing.