x dx V21-(x+3)² 1. Complete the square to get S and then use the substitution x + 3 = /21 sin u so that dx = /21 cos u du.

Q: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

A:

Q: solve the following x cos?y dx+tany dy = 0 -Q1 y dx = ( x+Vy2-x² ) dy -Q2 (sine - 2r cos?e ) dr +r…

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Q: d² dx dx 3. di² +2 +5x = sin 21, given that when t = 0, x = 3 and dt dt 53 [ 55 Ans. e 17 cos 2t + -…

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Q: Q5-Find for x? + cos(xy) = y dx

A:

Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: S V3x – I dx а. - b. f cos 7x dx J 2+sin x COS x dx с.

A: As per our guidelines we are supposed to answer only three subparts of a question. Kindly repost…

Q: dy 5. Find : (b) y = cos (11x³ + 5x). dx

A: The detailed solution is given below Thank you

Q: 7 Cos X dx e 4 Using the Midpoint Rule, M(50) =| |: %3D

A:

Q: y=(4x -5x +6)(e-sin 2x), then find dy at x 0.

A:

Q: Q1: Find 1) e (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 4) l (3t5) 5) e (est + cos 3t)

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Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: Integrate the following using the substitution method. a) Te* cos e dx 2x+1 3x² +3x

A: We will use substitution method to evaluate these integrals.

Q: The function y = 4e3x sin x is a solution of dy = 3y + 4e3x cos x dx A) True B) False

A:

Q: c. T(x) = x (**-cos(2x)). find Q at x = t/4. d. T(x) 100e-3x + In(4x), k=470, A= 0.01r and x= 1/3;…

A: c) Given, T(x)=x(x2-cos(2x)) at x=π2

Q: Q4: Find dy\dx if|cos?y +5y2 = x2

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Q: x2-y2 dy 8. dx du Y: Formula: J Ta?-u² = sin-1 u V a

A:

Q: d²y Given that y = -4x cos 2x +4 sin 2x, find dx² at x = 2

A: Given: y=-4xcos2x+4xsin2x

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

A:

Q: Q;: Find for the following functions: - dx xcos (x³+1) 2- y = Tx cos" (x³+1)

A:

Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

A:

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

A:

Q: If x = 3 sin t and y =2 cos* t , then find dy at t = dx 4 O a. -0.67 O b. 0.76 O C. 0.56 O d. -0.86

A: Given x=3sin4t   ,y=2cos4t

Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: Can you help me step by step?

A: The derivative of a function is computed as follows.

Q: Find dy : (a) y = cos(1 Ix + 5x) dx

A: Topic:- calculus

Q: Q3: B find dy/dx for the following equations : 1- y= e(3-cos4x) cot 3x 2- y =- 2x+sinx

A: Given 1)  y=e3-cos4x2)  y =cot3x2x+sinxwe have to find the derivative

Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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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: dy cos3x, at x = 1.5 is approximately: dx Given y Select one: А. 2.933 В. —0.235 C. 0.235

A: y = cos3x Differentiating dydx= -3 sin3x

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

A:

Q: 2 S² T ㅠ 1-cos x dx 2

A:

Q: Q4: Find dy\dx if|cos'y +5y? = x?

A: The given equation iscos2y+5y2=x2to find dydx

Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: 4. Find d?y/dx² for the following functions: a) y = sin x² cos 2x b) y = cos*(sec² 3x) c) y = x²(x³…

A:

Q: Q) Find the general solution. dy sin-1x Iny dx II

A:

Q: x dx 1. Complete the square to get J 21-(x+3)² and then use the substitution x + 3 = V21 sin u so…

A: The given integral is: ∫x dx21-x+32 To evaluate this integral, substitute  x+3=21sinu…

Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

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Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

A:

Q: The function y = 4e3x sin x is a solution of dy Зу + 4е3х dx COS X %3! (A) True (в) False

A: Differentiate y with respect to x

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

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

Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

Q: به)ک ن ان -)f Ssin*(x)cos°(x)dx du )کی + 207 - )J No appropriate Match au)قی - 207 - ه-)J du )کی +…

A: Find the integral match of the integral sin5xcos5x.

Q: D. ( [ 3° cos"(5t) dt sin(z)

A: