Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

Q: H.W: Use the Trapezoidal Rule with n=6 to approximate. Here f(x}=sin2x,a=0,b=x.

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Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

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: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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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).

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Q: S sec" (0) tan" (0) do is u = tan(0)

A: Evaluate ∫sec10θ tan8θ dθ

Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: Н.W 是, and , if ay Find ax Je az 11. f(x. y) = sin(y- x) 12. f(x. y) = tan %3D %3D por

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Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

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: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: dz az Find and of the equation z = xy arctan ax ду

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

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: 3) if y= CoSX then shift it by a) left TC b) Down1, lett 2

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Q: Find in terms of x and y if arctan(r + x²y) = ry

A: Given that         arctan(x+x2y) = xy We have to find dy/dx in terms of x and y.

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

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

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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: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

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Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: Given, a(x,y,2) = 23x3 tan (y) + x*29 %3D Find the expression for Izyz and Caleulate it at the point…

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

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: Show that w°sin(xw) пе dw= 2 cosx if x > 0. w* + 4

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Q: The length of the curve y = In(cos x), 0< x <:

A: To determine the length of the curve, y=lncos x, 0≤x≤π4.

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

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

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: If 1-x V1+x y = Tan where |x| <1, then find dyldx.

A: Given y=Tan-11-x1+x. We need to evaluate the differential of y with respect to x. Tan y =1-x1+x…