Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

Q: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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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: -1 Differentiate y = sin (sec(4x?)). %3D 82 tan(4a?) sec(422) A. y' 1-sec2 4r2 8æ tan(42²) sec(4x²)…

A: We will find the derivative of the given function in the following step.

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: Evaluate the integral tan 4x dx tan? 4x - 24 nltan- O inltan 4x + Vtan? 4x – 24| + C 1 Arcsec tan 4x…

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

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Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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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: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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

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

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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

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Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

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

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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: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: 4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: show that1) d/dz [cosz] = -sin z

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Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

A: Given that csc(2x+30°)=cos(3y-15°) It is known that csc(x)=1sinx. So, 1=sin(2x+30°)cos(3y-15°)…

Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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

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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: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2>0 then…

Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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