7 (2+ x³)' Vx² – 1 (x2 + x + 1)* 3 d B : dx - 4

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: 8x + 5 Split the integrand I dx into two parts. 8x + 5 dx 1 - x2 8x dx + 1 - x2 V1- x2 2x 8x + 5 dx…

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Q: Fina aly for y = 3x V3-x4

A: we have to find dy for given y

Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: 9-x² dydx. 2

A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: ential equati x²y dy = C

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Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: solve using reduction of order (D^2+1)y=tanx

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Q: / (6x" – 7Va+ 19x- 8 -- + Evaluate + 14e0* + V11 dx. (You don't have to show the work.)

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Q: Wt-1+2 dt

A: We will find the integral as following.

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: 2. Find an estimate of the root of the equation: 2* + vx² +5=20 using regula-falsi method. Ans x:

A:

Q: What is the integrating factor y x² = 2 (2x - y)?

A: The given equation is; y'=2(2x-y).

Q: [(2-sec²x) elnate sec³x dr What should be the value of A for to be integrable using the formula 'du…

A: Let's find.

Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: (5tan28 etan 28 sec² 2 Bd B

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Q: 11. Integrate. a. x3 b. S(5 tan 3x – 2 sec2 x)dx

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Q: 1/2 x3 dx 1- V3 - 15 15 2 16 Option 1 Option 2 1 15 V15 16 8. Option 3 UOption 4 IN

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Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

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Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

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Q: Integrate the function. Vx2+36 dx 5x2 Select one: A In x2+36 А. 1 + x/ - Vx2 + 36 + C 5х В. Bx + In…

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Q: Find upper and lower bounds for

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Q: I need to integrate 1/(sqrt(a^2+x^2)). If I let t=x+sqrt(x^2+a^2) where t>0, then how do I…

A: The given integral is,

Q: Sec-S 2 1 TanOLO

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Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: Y2-1 dy

A: Follow the procedure given below.

Q: (12z – 12z2 + 71z – 77 Integrate: 4x2 + 25 - la( |42° + 25|) – arctan X + C

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Q: tion k passes through the points (4.

A: Please refer to the image below

Q: Find 2. dy of 2.

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Q: 3cos3x-1 uate f dx, the integrand can be tran 1-sin2x Bcos3x + csc²x)dx

A: We have to choose the correct answer from the given options according to the given information

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: у %3DIn(In sec x)

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Q: prove that (d/(dx))(sec^-1x)=1/(xsqrt(x^2-1))

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Q: Find without using the Chain Rule

A: The given differentiation is:  ddxlnx101 To evaluate the given differentiation, apply the…

Q: Use the method of Variation of Parameters to solve. SHOW WORK. у" - у' — 2у %3D 2е-t

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Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: Number 8

A: first find the derivative.

Q: 2an-butn Converge bey to

A: The given sequence is an.bnn=1∞ we observe that there is N1>0, so that when n>N1, we have…

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

A:

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: A golfer makes a successful chip shot to the green. Suppose that the path of the ball from the…

A: Please refer to the image below

Q: sin(3z+z²) Find y' for y = (6 – 2*)3

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Q: J7 -dz 21-8

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Q: 4. Use integration by parts to evaluate (2x - 5) cos(5x - 2)dr.

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Q: 4x2-3 f (x) 2х3+x2+7

A: