7. Find the derivate of the following, i.e. Find y 2In(r)tcotfe) 2 t sin(t)dt (d) y =

Q: 3. Use lhe Intermediate Value Theorem to show that dhe following equation has a solution. sec(x) =…

A: Given secx=x^2+e^e-1

Q: need help with attached, thanks

A: Given function and interval are,

Q: Find dz/ax andðz/@yif I z = x* sin(xy³).

A: If a function f(x, y) is to be partially differentiated with respect to x, then we treat the…

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: (-8 sin(t) + 8 cos(t)) dt 0.

A:

Q: 1. Given that x = 3 cos nt, y = 3 sin at and z = 4nt with 0<t<1. Evaluate (x + z) ds.

A:

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: 29. (x² + y²) ds Jc C: r(t) = (1 – sin t)i + (1 – cos t)j, 0 < t < 2n

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Q: You tart muesting at t=0 y co) =0

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Q: a. 9(t) = | (2(t – 1))' sin(4r) dr L{p(t)}(s) = ct b. y(t) = -7(t-T) cos(77) dT L{p(t)}(s) = %3D c.…

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Q: 3. Differentiate the following with respect to the variable: a. y =-2 Lnx – cos 5x + 6 sin 2x – 2 x²…

A:

Q: 1. Find for the following: dr a. r° + y³ = 8 b. y sin y = ry c. tan-'(r+3y) = rª

A: According to our guidelines we can answer the first three subpart for you ,you can ask the remaining…

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: 2 6 Use Fubini's Theorem to evaluate 2x exy dx dy. 00 26 2x e Xy dx dy = | (Type an exact answer.)…

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Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: 24.(cos t) y″ + (sin t) y′ − ty = 0

A:

Q: 2. Find dz/dr and dz/dy. (a) x² – 3yz + xyz – 2 = 0 X (b) ye“ – 5 sin 3z = 3z

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Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: y = sin x, y = cos.x , x= 0 , x=- is revolved about the x-axis T/2

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Q: (2) Use appropriate substitution to solve the following 1-1-y dy (i) dr tan (x+ v). (ii) y = %3D z+y…

A: As per our guideline we are supposed to answer only one asked question with first three subparts.…

Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: 1. Find the following antiderivatives: (b) (cos(5e) - sin(21)) dt eat (c) -2t dt 2

A: As per guideline we have to solve only three

Q: rION 4. Find du/dt for the following: 35. u = tan-(xy) ;x = sin t;y = sect x-y 36. и 3D In ;x = sec…

A:

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: 16. a (t) = sin ti+2 cos t j + 6t k, v (0) = –k, r (0) = j – 4 k %3D

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Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

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Q: B-The result of dy/dx for the following function is COS X y 1+sin x

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Q: Eliminate the parameter t from the following. (x(t) = 5 + 4 sin t y(t) = 2 + 2 cos t

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Q: 4.1 z+ cos(T2) dz, z(z² + 1) with C: |z – i| =.

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: N 1 1 202 2{(xn – µ)²}– z(Ord – r). n=1

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: 2n 37 So² S67 (x sin(y) – y cos(x)) dxdy = %3D

A: The given question can be solved as shown in step 2.

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

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Q: dz Oz d'z az dx'dy' dx2' dy2 Q2. Find for the following: a) z cos(2x + 3y) b) z - x sin(2x+3y)

A: To find the partial derivatives of first and second order of the given function

Q: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: 1+ cos(t) 1 – sin(t) 2t) (n) y(t): (o) y(t) = In(5tª + 3t2 + 1) (p) y(t) = t° + T' + e™

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Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: .2 Q3 Suppose that w = Jx2 + y² + z² e" cos 0, y = e" sin0 , z = re® Find aw and ar aw дө

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Q: Given dy find y 6 cos 6x dx O sin 6x + c O 6 sin 6x +c O-6 sin 6x 0-36 sin 6x

A: Given problem is :

Q: 5. Evaluate r'sin(y³) dy dx

A:

Q: 5 Find *: (a) y = cos(11x + 2x) dy

A:

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

A:

Q: (a) Find dr dy given that x²y + sin xy = 0.

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

Q: Solve the following differential cquations 1. x + x*y -sec(xy) Ans. sin x = 2x2 +C x +y Ans. y- tan…

A:

Q: 4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

A: Okay I am explaining the marked step.

Q: 3. Evaluate L{4e¬2tt3 +t sin t cos t}

A: