Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²)…

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Q: test for the exactness of the differentral dy + Cosx +Sinyfy -0 quation And hence find the Salution…

A: A differential equation contains independent variables, dependent variables, and the differential…

Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

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Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Show that both y = sin x and y = cos x satisfy y" = -y.

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

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Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

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Q: Determine the constants a and b such that                                                       sin…

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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: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: b,c,d

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: Differentiate y = In ( sin² (4x)). A y' = 8 tan (4x) y' = 8 cot (4x) y' = 8 csc2 (4x) sin (8x) y' =…

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Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

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Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. tan2y dy = sin3x dx

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

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

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: I) Find the volume of the solid obtained by rotating the sine function between x -0 and x x about…

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Q: d'y +2 sin y cos' y = 0. dx 6. If y= tanx, show that

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Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: トキ 4 Sin Yx cos? dn SinYy

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Q: What is the antiderivative of sin^2(x) + 2sin(x)?

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

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Q: 2. Find the linear approximation to hly)=sin(y+1) at y=0. Use the inear approximation to approximate…

A: linear approximation.

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: gives – sin(y)ÿ = cos y = x, so implicit -1 - csc y = rentiatio dy dx

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Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: sin³€ dt to ylomeldon 3.

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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&gt;0 then…

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

A: