Example 9.16. A light elastic string stretched between two fixed nails 120 cm apart, carries 11 loads of weight 5 gm each at equal intervals and the resulting tension is 500 gm weight. Show that the sag at the mid-point is 1.8 cm.

Q: A spring with a 2-kg mass and a damping constant 8 can be held stretched 1 meters beyond its natural…

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Q: The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

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Q: QUESTION 17 The volume of the solid generated by revolving the region bounded by x² = 4y b formula…

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Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Using differential

Q: find the solution of the expression y(x) with the power Series in x=0?

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Q: The region E between the paraboloid z = 1 - 2² - y² and the plane z = 0 is shown in the 3D model…

A: We will use cylindrical co ordinate system to find volume

Q: 5 6. (s+3)² 7. 3 s2-32 8. L{f(t)}: 3s²-1 s²+8+1

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Q: The linear transformation Z: M2x2 (R)→ M2x2 (R) satisfies z = [₁₁3] ² [²D=[²₁²] ² D=[¹² 1. Solve for…

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Q: s these functions O(x) ? f(x) = 10 f(x)= 5 logx f(x)= x2+x+1

A: The big O notation is very significant in analyzing a function. It represents the efficiency of a…

Q: Question 2: Find the inverse Laplace transform of 10 a) F(s) == s(s+2)(5+3)² s² b) F(s) = 2 s² +4s+5…

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Q: Z = (1 - j)¹-2j

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Q: H) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent the…

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Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Example 10.2. Find the value of y for x = 0.1 by Picard's method, given dy y-x dx (P.T. y + x³y(0) =…

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Q: POSSIBLE -10-8-6-4-2 -X 8 10 -2 -4 -6 -8 10 Triangle LMN is reflected across the x-axis, then…

A: Direct calculation.

Q: 2- Every finite set in any topological space is:

A: every finite set is any topological space is COMPACT

Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: Convert + [²√¹²5² √²¹²²²³²²³² (x² + y² + 2² )dzdxdy into an (x² + y² + ²)dzdxdy √18-1²-² coordinate…

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Q: Let f(x) = (3-3x) 5 f(x) has one critical value at A = For x A, f(x) is Select an answer ✓ Select…

A: Solution:-

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: The real part of csch (2-j3) is O -0.5118 O none of the other choices O -3.5906 O 9.8844 O 1.0357 O…

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Q: Let B B-{B·[3]} and B-{[4]-8} B' Suppose that [32] A = 4 is the matrix representation of a linear…

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Q: Exercises To Solve [No.5] Lim 5 9-5 dx -x²8x-15 D "Cosx dx Sin x+25inx+5 b

A: 5)  Let , I = lima→5 ∫a-4 dx-x2 - 8x - 15 Let , us simplify denominator first ,  -x2 - 8x - 15 = -x2…

Q: When mathematical models are used to describe process dynamics in conjunction with control system…

A: Solution:-

Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

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Q: first 4 terms of the Taylor series for : f(x)=sin лx near a=0.5

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Q: Example 10.12. Solve the following by Euler's modified method dy = log (x + y), y (0) = 2 dx. at x =…

A: Solution: Given, y'=log(x+y) y(0)=2 Applying Modified Euler method: f(x,y)=log(x+y)…

Q: ule? How to solve by both methods? Ju he final answer

A: solution find using trapezoidal and simpson 3\8 rule

Q: Find the 4-point discrete Fourier transform (DFT) of the sequence x(n) = {1, 5, 3, 1}.

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Q: Evaluate f(x²y+3xyz) dxdydz by applying the transformation u = x, v=xy and w=3z, where G is G region…

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Q: By using the method of least squares, find the best line through the points: (2,-3), (-2,0), (1,-1).…

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Q: Question 20 Evaluate ·S= A B C D 3x5 3x4+6x3-3x2 - 6x x+In[ + In -dx. using method of partial…

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Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

A: There are so many subparts, as per our guideline we can solve only first three subparts. Please…

Q: Prove that span (v1,v2,...,vn) is a valid subspace of R

A: Let V = R is a vector space. Let S = v1 , v2 , ..... , vn We need to show that   span(S)  is…

Q: Determine why dx converges or diverges.

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Q: 2) Consider the function a(z) E 50 *>0 3 > 0 a) Let f(x) = Is f Riemann Stieltjes integrable with…

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Q: Example 12.5. Find the maximum value of Z = 2x + 3y subject to the constraints: x + y ≤ 30, y ≥3,0 ≤…

A: The linear function that needs to be optimized(maximize or minimize) is called the objective…

Q: QUESTION 19 The volume of the solid generated by revolving the region bounded by x2 = 4y method. The…

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Q: A Norman window is in the shape of a rectangle surmounted by a semi-circle.

A: We have to solve given problems:

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

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Q: Example 10.33. Applying Euler's method to the equation dy/dx = hy, given y(x) = yo determine its…

A: We need to solve this problem using Euler's Method.

Q: 3x 2x13x2x3 = 0

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Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Example 12.5. Find the maximum value of Z= 2x + 3y subject to the constraints: x + y ≤ 30, y ≥3,0 ≤…

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Q: Use Simpson's Rule to evaluate the following. n = ·3 1 dx 1 + x² 2

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Q: I'h[f(xo) + f(xi) hip. + fino T p1- 호 Fer

A: We derive the trapezoidal rule for approximating                               ∫abf(x)dx

Q: Find the angle a between the vectors α= | and

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