"y=sin't+ tant, x=- In-cost)-e Snt, find the value ofy when t= 6/2 2-/2e 2 3/2 1 2+VZe V? 6. -Vle

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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Q: 1. Approximate | sin(x²) dx with 12 subintervals by Trapezoidal rule. 1 Simpson's - rule. (a) (b) 3…

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Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

A:

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

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Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: the length of the curve y = coshx 1sx<2 is sinh(2) – sinh(1) Select one: O True O False

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: of the tangent line to the sine function at the origin. y y= sin(7 x) values with the number of…

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

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Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Ni cos(2?)a. Cos | x dx

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

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Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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Q: eteR MiNe SiN IN°()COS)dx

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Q: 19. i) Differentiate sinx with respect to x from first principle 1+3x dy ii) Find, dx when a) y (x…

A: Part i,Given,          fx=sinx

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

A:

Q: 3. Find tangent line to x = 2 cot 0 y = 2 sin? 0 at 0 = t/4

A: First  differentiate  and find slope use equation of tangent line

Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: we have to check the DE sin(x) +y cos(x) = 1 for Exact then My= dx None of These - sin(x) sin(x)…

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Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: 2. Solve for general solution using exact method. (cos x cosy – cotx) dx – sinx siny dy = 0 %3D

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Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

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Q: 10.y = Arc cot (sinh3x) 11. y = cosh?4x - cos 12. y = In (sinh4x) cosh8x +x² 2

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) /…

Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

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Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

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Q: Cualuate the definle integial. x33 COs (xH) dx

A: