The sutiable substitution for evaluting csc' (x)cot (x)dx is (a) u = tamx (b)u = cot x (c) u = cscx (d) u = secx (e) None a C d e

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

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Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

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Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

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Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

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

A: Topic = Derivative

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Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

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Q: Show that sec x = (sin x / cos x) + (cos x / 1 + sin x), then use the identity to drive the basic…

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Q: d arctan (tanh x) dx Show that sech 2.x.

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Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i -3j b)…

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

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Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: Find the derivative. y = sinh 1(tan x) O y = |cos x| O y = 1 /1+tan x O y = 1 Vtan? x-1 O y = |sec…

A: In this we have to find integration and derivative.

Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

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Q: tanx 4) S Edx Cosxv1+secr 5) S(1- u)vudu

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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A: The given question can be solved as shown in step2.

Q: 4. When a 2-kg block is suspended from a spring, the spring is stretched a distance of 40 mm.…

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

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Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: A beam of length L is embedded at its left end and simply supported at its right end. Find the…

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Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Suppose a particle has velocity given by v(t) = sin(t). What is the net displacement of the particle…

A: GIVEN DATA : Velocity of  the particle v(t)=sin(t)        TO FIND : Displace of the particle on 0,…

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy

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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: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

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Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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