1. Use the Euler, improved Euler and Runge-kulta methods to Solve the folllowing ODE s: 42 y =0 C. y co) =1, h= 0.2 O -

Q: DO NOT include spaces in between 17 characters. * Compute m d (In (In y)) at y=e. dy Your answer

A: The objective is to compute the derivative at y=e.

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: (a) Oppositely directed to v = (7, –20) and half the length of v. 7 V449 -20 w = 898 8. (b) Length v...

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Q: 3. The statement f(x) dx = [ f(y) dy is, A. true B. false C. sometimes true D. neither true nor fals...

A: Given,            The statement is ∫abfxdx=∫abfydy.To find : Check whether the statement is true of ...

Q: Find the area of the parallelogram that has u = i – j+ 2k and v = 2j + k as adjacent sides. NOTE: En...

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Q: S 30x° e -x 10 dx 30х е 8. 8-

A: Let x10= t  Derivating both sides  10x9dx= dt  

Q: etermine f(x) given that f'(x) = t* – t³ + t2 +t – 1

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Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

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Q: 1. A Norman window is constructed by adjoining a semicircular window to the top of a rectangular win...

A: We have to find the dimensions of the given window.   According to our guidelines we can solve only ...

Q: DO NOT include spaces in between characters. Compute g'(2) if g(x)=10**-2*. 16 Your answer

A: The objective is to compute g'(2).

Q: x+2 8) Let f(x) = values of x at which the function is discontinuous. Determine the +x – 2 Determine...

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Q: The rose r = asin 30

A: Solution is given below:

Q: Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). (a) Find the volume of th...

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Q: + x° rp („z +

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Q: Evalnate the fo llowing limits 1. lim 4x-5x+1 メ→ -4x? 2. lim I x²+5x -6 X- 4 lim (1x-7)* 3. 2.

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Q: 1: Find the area of the region bounded by the graphs of x = y², y = x + 3, y = -3 and y = 2.

A: The region is bounded by x=y2, y=x+3, y=-3 and y=2

Q: 1. find an equation of the line tangent to y = x-3 at point (O,-) %3D

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Q: The slope of the tangent line to the curve y 2x at the point (- 5, - 250) is: The equation of this t...

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: Find the arc length of the parabola y² = x from (0,0) to (1, 1). (Note that y² = x is not the same t...

A: Length

Q: rtoo Е. re dx स०२२

A:

Q: Find the vector component of v = (4, –1, 7) along b = (6, 6, –7) and the vector component of v ortho...

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Q: Find the area of the triangle with vertices P(1,2, –3), Q(0,0 R(3, 5, 1). NOTE: Enter the exact answ...

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Q: Find the derivative of g(x)= using the limit definition

A: Solution:we have use formula g'x=limh→0gx+h-gxhgx=1x-1g'x=limh→0gx+h-gxhg'x=limh→01x+h-1-1x-1h=limh→...

Q: - Evaluate the following integral. |e2* cos3x dx

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Q: 4 + 2y - 16) dy =

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Q: Consider the points A(3, – 1, 3), B(4, –3,0), C(-2, –2,0), and D(6, 3, –5). (a) Find the volume of t...

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Q: Evaluate the given integrals. dx 3. Csc 3x-cot 3x

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Q: Find d'y /dx? Y = xtan (=)

A: d²y/dx² means we have to calculate second derivative of the function.

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A: Find your answer below 

Q: 3. At midnight, the heater inside your house breaks down. The temperature (T) inside your house at t...

A: dTdt=-k(T-T0)∫ dT(T-T0)=∫-k dtln(T-T0) =-kt+ln CT=T0 +C e-ktat t=0;T(0)=21°CT0 =-6°C21=-6+CC=27T=T0 ...

Q: The slope of the tangent line to the curve y 2a at the point (- 5, – 250) is: The equation of this t...

A: here for slpope we have to differentiate function y =2x3 dy/dx = 6x2 slope at (-5 , -250) dy/dx = 6(...

Q: y = 3x2 from x = 1 to x = 2.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 40 v cos 40 d0

A: We can find the integral as below.

Q: Note: Values of x should be typed in INCREASING order from LEFT to RIGHT. DO NOT include spaces in b...

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Q: Find two unit vectors in 2-space that make an angle of 45° with 10i +3, NOTE: Enter the exact answer...

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Q: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal ...

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = t2i 1,3K 4tj + %3D (a) r'(t) (b) r"(t) (...

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Q: Test II. Match the definition in column A to the corresponding theories in column B. Column A Column...

A: Find your answer below 

Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy ...

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Q: explain

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Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y

A: area of the bounded by the y=1+lnx3x

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region a...

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Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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Q: 8. 15 Use the figure above to find the exact value of sin 20, cos 20, tan 20. sin 20= cos 20= tan 20...

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Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v ort...

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Q: 8. A curve whose slope at any point is 6x² А. у %3D 2х3 — х? +х+6 - 2x + 1 passes through the point ...

A: We need to find equation of curve.

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

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