I Graph the functions in Exercises. of the function on the interval and say where they occur. . Then find the extreme value 71. f(x) |x- 2 + x + 3, -5 sx 5 72. g(x) = |x 1| - |x - 51, -2 sxs7 73. h(x) = |x + 2| - |x - 3|. -0 < x< 00 74. k(x) = |x + 1+ x 3, -00

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A: To find The constant C which satisfies the given initial condition y(1) =1

Q: Choose the Laplace transform of the given function. 8 (t – T) t cos (t) e-TS + T -TS e TS -Te те

A: Laplace of δ(t-a)=e-as We also know x(t)δ(t-a)=x(a)δ(t-a) so t cos(t) δ(t-π)=π cos(π) δ(t-π) = -πδ(t...

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A: We have to find the power series of f(x).

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another in...

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two...

Q: (b) Find the area of the triangle whose vertices are A(0,0,0); B(1,1,1) and C(0,2,3).

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Q: • Exercise 2 Assuming that i) the sequence of functions {f„(x), x € [0, 2)} converges to f(x) in L2[...

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Q: Se xye" dy, C. x- , y-, z- , 0 <te1

A:

Q: Given points P(5, 2, -1), Q(2, -3, 0), T(4, 2, 4) foms the triangle. Find the interior angle at Q

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Q: Use Euler's method to calculate the first three approximations to the given initial value problem fo...

A: For the solution of the problem follow the next steps.

Q: System of Lincar Eauation Slope Intercopt form Slope (m) Y- Intercept c6) 2x +y = 5 y= -2x +3 2 + y ...

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Q: Q5: Use the method of variation of parameters to find the general solution of the et differential eq...

A: It is given that y''-2y'+y=et1+t2+3et. We have to find the general solution of the given differentia...

Q: 3. By the method of least squares, fit a curve of the form y = ax + bx2 to the points: -1 1 2 3 y -3...

A: We need to fit a curve of the form y =ax +bx2  So we can use  ∑i=1nxiyi=a∑i=1nxi2+b∑i=1nxi3  ..........

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A:

Q: N! sin(B t) s2 + B2 cos(B 1) s2 + B2 N! (s - A)N+1 B A sin(B t) (s - A)? + B2 S - A Ai cos( B t) (s ...

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Q: Evaluate the two integrals given the graph. The two parts of the graph are semicircles. f(x) dx and ...

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Q: The volume of the solid bounded above by the paraboloid z = 4 – x? – y? and bounded below by the par...

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Q: Solid Con Sist of ight hi aud a cylinder of hrinlt ha the dim ensieua

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A: Third option is correct one.

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Q: the derivativc Of R (E) =

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Q: Consider r² – 2x +1 if r 1. Determine if the following functions are continuous on the interval I. ...

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Q: 2 has a critical point (equilibrium solution) xe = .3 The system of DEs x' x + 1 True O False

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Q: 1z 2x² + y%, (1) z = 2 y;

A: Solution:-

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Q: 0 hours. Water begins to be pumped A tank has 15o liters of water in it at time t into the tank at t...

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Q: Q/usethe Fibona ccimethod to Solve thefrablem In four stefs uPslon Min fo=X+ [ze27,6-1] and E=ort 25...

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Q: Advanced Math Let R be a PID and let m be a maximal ideal domain in R. Let F denote the field R/(m)....

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Q: For the equation below, solve for the following. Use a calculator to approximate all answers to the ...

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Q: dy * - x Iny; yc1)= |

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Q: 5. Determine the roots of the complex numbers studied in class. z³ = 2 – 3i

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Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

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

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

A: This is the problem of vector algebra.

Q: What type of roots are shown in the following diagrams? i) to this ii) IIIJ

A: This is a problem of nature of roots, application of differential Calculus.

Q: (2) Show the argument below is invalid (¬q ^ r) → ¬8 -pAr 8 V p^m .. 8 m

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Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Lu, by grouping the ...

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Q: Consider the differential equation y" +9 y = 6 (t) +8 (t-2) for a system that is initially quiescent...

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Q: Let f(T) and g(T) be polynomials in Q[T] whose gcd in Q[T] is 1. Show that 1 is also their gcd in C[...

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Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: 2. Calculate the Laplace transform L{12e cos²(3t)}.

A:

Q: a=15 b-18,C=20

A:

Q: 4. Use the dilation principle to find the Laplace transform of 1- cos 5t cos t given L{- In g² +1 t

A: We want to find Laplace transform of 1 - cos5tt Given L1 - costt = 12lns2s2+1

Q: Hiwi fined the curvature for each the Fllbwing vector function Pt) =(44,-t, 2f>

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