Let h be a differentiable function. Also he [a, b]. Prove that there is a sequence {x} = (a, b)such that xn → a and f'(xn) → f'(a)

Q: Express the following in a + ib form a. (4i-7)+(2+i) b. (5-2i)(2+ 2i)

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Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: Example 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

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Q: use Cauchy's residue theorem, where appropriate, to evaluate the given integral along the indicated…

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Q: Solve for the laplace transform. Show your solution.

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Example 11.10. Solve the boundary value problem u, u under the conditions u(0, t) = u(1, t) = 0 and…

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Q: 2y"-3y"- 3y + 2y = (e*+ex)²

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Q: If F is a finite field of characteristic p, then aap is an automorphism of F.

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Q: 1.1 2. t 3. e3t 4. t sin 3t 5. et sin 3t

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Q: (a) Find all roots of the quintic equation, in the complex plane and plot them. 25 -1 = 0,

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Q: Example 8.8. From the table below, for what value of x, y is minimum? Also find this value of y. 3 5…

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Q: B. Compute the shared mass between the polar curves (r = 1+ cose) and (r = 1- cose), usę density…

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Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

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Q: Q1. In process to prove that f(x)=sin(x -x]) is continuous, we apply the composition of two…

A: We know that the composition of function is defined as (g o h)(x) = g(h(x))

Q: 5) Suppose that f(0.75) = f(0.25) = ß if the composite trapezoidal rule with n=2 gives the value 4…

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Q: Determine one real root of 2xcos2x - (x - 2)² = 0 on the interval (2, 3) using the Bisection Method.…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 鼎 3) Find the derivative f(z) = a) f(z) = 400z(z²-1)" (z²+1) b) f(z) = 400z(z²-1) (2²+1)100 c) f(z)…

A: I just used the chain rule and product rule for derivatives

Q: 1.Tony is 6 years older than Jonathan. Six years ago, she was twice as old as he. How old is Tony?…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

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Q: Using the power series method about x = 0, the recurrence relation of the differential equation: y"…

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Q: g(x) 8/(x) Evaluate lim . W W W W . f(x) g(x) X . .

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Q: Suppose that f and g are both continuous functions. Also f, ge [a, b] and b that f f = fg. Prove…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Solution : Area calculation between the curves, y=x(x-4)(x-6) and y=0 Intercepts of cubic equation…

Q: Example 12.14. Find an optimal solution to the following L.P.P. be computing all basic solutions and…

A: The problem belongs to the concept of L.L.P.

Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Q=∫02∫-4-y20∫x2+y28-x2-y2ydzdxdyRegion of integration,0≤y≤2-4-y2≤x≤0and x2+y2≤z≤8-x2-y2

Q: A space vehicle flies into a gravitational force field F(x, y, z)=-y(b²2² + a²y²)i + (b²r² + a²y)j…

A: The work done by a force field is equal to the dot product of the force field and the displacement…

Q: A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the…

A: Given that there are two cars. First car has fuel efficiency of 25 miles per gallon of gas. Second…

Q: Find general solutions 17. y" - 4y = -12r² +6x-4; 18. y"+y+y = -13 sin(2x); 19. yy=e+xz; 20. y" - 4y…

A: 19)  We have given a differential equation ,  y'' - y = ex + x First we will find complementary…

Q: from Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy 2xy +…

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Q: y"-3y¹+2= 1²+5t-2 1. Method of Variation of Parameters

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Q: Evaluate the double integral that will solve for the area of the region bounded by y = cos(x) + 5, y…

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Q: Q10. Using Corollary 3.1.24 of the book, to prove that a graph G is bipartite if and only if a(H) =…

A: Given: α(H)=β'(H) To find: Isolated vertices

Q: Solve for x. All final answers must be in Znwhere n is the modulus.   x+ 2 mod 9 ≡ 0

A: We have given that ,  x + 2 mod 9 ≡ 0 We need to find the value of x under modulus 9. We know that…

Q: Construct an angle XYZ of 105° with YX = 93 mm and YZ = 70 mm. Measure the length of XZ.

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Q: Let D be the portion of z = 2x + 5y inside z2 + y² = 1, oriented up, and let F = (y, z, -z). Compute…

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Q: 1/3 y = x¹, x = 0, y = 1; about y = 2

A: As per the question we are given a solid of revolution which is obtained by rotating the area…

Q: C: 2: Find the first 4 terms of the Maclaurin series for : In(1+x)

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Q: The real part of sech (2-j3) is -3.7245 -3.5906 O 0.0403 O -0.0106 -0.5309 1.0357

A: The Euler's formula is widely used formula in complex analysis. It makes a bridge between the…

Q: Example 10.6. Solve by Taylor series method of third order the equation dy dx y(0) = 1 for y at x =…

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: is R* is contractible?

A: This is a problem of Topology.

Q: 2Using the spherical coordinate, find the volume of portion of the sphere Jutub x² + y² +²=9 lying…

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Q: 1) Let S be the equivalence relation on R defined by xSy iff x-y Q. Then a) [√3]-(-√3+r,req) b)…

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Q: constants. ple 9.2. From y₁ = A2" + B(− 3)", derive a difference equation by eliminating the

A: Given, yn=A2n+B(-3)n   1 Replacing n with (n+1) and (n+2) in the above relation…

Q: (Signal And System) Question 1. The real system example given below 1-Extract the equations of the…

A: Solution: From the problem statement, m.v˙+b.v=u  .......i where,           m = mass…

Q: Evaluate the line integral along the curve C. 1. 21 10 21 2. 20 21 3. 20 8 ds, C is the curve r(t) =…

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Q: If K is a field and if 1, 2 are distinct automorphisms of K, ther it is impossible to find elements…

A: This is a problem of Abstract Alhebra.

Q: Suppose that f and g are both continuous functions. Also f, g € [a, b] and that f= fg. Prove that 3c…

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Q: Solve equations: 10. y == y x+y 8. y 3y+M(1;1) x M (0; 0). -; 9. xy = x + 29: 11. g =2ry+1;M(0;0)…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…