a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Find all the singularities of tan(z) f(2) = determine their types, and compute the residues at the…

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Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

A:

Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: 2 = using the relation r= VT show that sin x %3D EX II

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Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

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Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: Use symmetry to evaluate the followingintegrals.

A: Given:∫-11 1-x dxIf f is an odd function f-x=-fx∫-aa fx dx=0If f is an even function f-x=fx∫-aafx…

Q: Having f (x) = 1 +e¬* sin(4x) and the interval [0,1] Apply composite Trapezoidal and Simpson's rules…

A: I have done by the direct method and trapezoidal rule and find the error by trapezoidal rule

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

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

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: 4. Using the definition of sech x ,x 0 in terms of e , prove that 1+V1-x2 sech x = In ,0<x <1 Hence,…

A: 4) i)

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: The Wronskian, W, of the functions y1 = sin(2x) and y2 cos(2x) is %3D

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Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

A:

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: 5. Determine the GS of the first ordered linear DE dy (5 + 3y tanx) dx %3D

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Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

A: Given: ∫tan52xcos42xdx

Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

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Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

A:

Q: The approximation of I = S, tanx dx using composite Simpson's rule with n=5 is: O 0.6158 O 0.6236…

A: First option is correct

Q: Find y prime for y=(cos(x))^x

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: Prove that d/dx [cos x] = −sin x.

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Q: HiW Q Prove that : tanhclax) = x-! %3D x2+1

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Q: dy - y tan x = 10 tan x dx ution of y(x) using two different techniques. Hint: tan x dx = - In(cos…

A: We have to solve given problem: First method:

Q: Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

A: Multivariable function: When a function f has more than one independent variable and only one…