Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

Q: The Fibonaccis Sequence is defined so that F = F –1+ Fr-2. Given that F12 144 and F13 233, find F14,...

A: Given that  The Fibonaccis sequence is defined. 

Q: Find the exact area of the surface obtained by rotating the curve y =x2, 3 0<x<12, about the y-axis....

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Q: What is the Laplace transform of f(t) = te' ? AJ F(s) = s+ es %3! B] F(s) = 1/(s–1)² c] F(s) = 1-s/s...

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Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}. ...

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Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: Solve the sifferential equation using Ace Laplace transforms- y-3y'+2y=1-4X+2X y(0)=4, y'0)= 5-

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Q: Find the general solution to the following vector DE. 1 æ[t) = | -2 1

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Q: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of...

A: There are two Theorem by Pappus 1st for surface area of revolution and 2nd for volume of revolution ...

Q: 10x + 5y - 4z + 2w 6 x +y + 4z - 3w = 2 6x + y- 1 8z +5w 2x + 2y + 8z-w = 3 W

A: Given system is  10x + 5y - 4z + 2w = 6 x+y + 4z - 3w = 2 6x + y- 8z + 5w =1 2x+2y + 8z-w = 3 We sol...

Q: (x)f = „& y(0) = 0, y

A: This is the problem of Green's function.

Q: :Show that if every point of a surface is elliptic, then any curve C on this surface positive curvat...

A: This is a problem of differential geometry.

Q: now that 6z2 - 77y = 123456789 has no integer solutions for z and y.

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Q: Find the optimal Solution or optimal solutions for each of the following linear programming problems...

A: Given,         Max(Z)=40X1+80X2S.T.     X1+2X2≤60   4X1+3X2≤20and X1, X2≥0

Q: 9. True or False (T/F): If True, Prove it; If False, give a counter-example. a) For all nonzero nxn ...

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Q: 1 1. A = 1 2 -1 %3D -1 2 1 3 3 1212N 1.

A: We have to find the inverse matrix of the given matrix.

Q: Evaluate the following permutations by hand Find the number of permutations of 6 objects taken 2 at ...

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Q: (a) Milan is on a game show. He will choose a box to see if he wins a prize. The odds in favor of Mi...

A: (a) The probability of an event P in terms of odds in favor of the event is expressed as P=O1+O, wh...

Q: Use a linear approximation of f(x)=cos(x) at x=2π3 to approximate cos(123∘). Give your answer round...

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Q: Determine the day of the week on which January 1, 2020, will fall.

A: We have to find the day on week for the given date.  

Q: 4. mLA Yes 4x 2x

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Q: In an experiment 5 out 5 mutant mice developed cancer, and 1 out of 4 wild type mice developed cance...

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Q: 11. Find the coordinates of the center of mass of the solid bounded by the paraboloid: z = 4 – x2 – ...

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Q: n (-5)2η (j) n29n n=1 n (k) E(-1)"-1 in-1 yn n + 1 n=1 n νη + 1- νη-1 (1) E n=1

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Q: x² iy? Find points where f'(z) exist x+y Given f(z) %3D x+y

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Q: Apply Lagrange's formula inversely to obtain a root of the equation f(x) = U, given that f (30) = - ...

A: Here number of data points given = 4 and y = f(x) = 0  Also we have given x0 = 30, x1 = 34, x2 = 38,...

Q: 1. Determine whether the following sequences converge or diverge. If the sequence diverges, state wh...

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Q: i. Find the fourth order Taylor series expansion of the function, f(x) = In(x) around the base point...

A: I have attached the detailed step-wise solution in the following images. All the steps are written i...

Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical v...

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Q: Refer to Figure 1, find the Laplace transform of the function f(t) 1 f(t) b a a + b Figure 1: Functi...

A: Here first we write our function in terms of unit step function and then can use following formula t...

Q: 2. Q is an xn symmetric matrix, b is a vector of size n and c is a scalar If f(x) = x"Qx + b"x + c: ...

A: given  fx=12xTQx+bTx+c it is known that  gradient of the function can be expressed as ∂f∂xk=∑i=1nqki...

Q: Determine the root (if they exist) at the given interval for the equations as shown: x² – 2x – 5 = 0...

A: The root of the equation: f(x)=0 lies in the interval: a, b, if f(a)f(b)&lt;0. The bisection method ...

Q: Apply the Divergence Test, if applicable, to the series In 2n+5 n=1 Apply the integral test to the s...

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Q: 4 5 1 f = 4 2 3 6 7 3 6 2 7 1 (a) Write f as a product of transpositions (not necessarily disjoint),...

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Q: Let I be the flux of G = (5e", 7x°e",0) through the upper hemisphere S of the unit sphere. (a) Find ...

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Q: 2. Solve the following initial value problem in terms of g(t): y" – 3y + 2y = g(t) : y(0) = 2, y'(0)...

A: We can solve this using given information  

Q: 3. Water is being poured at the rate of 2 7 m3/min. Into an inverted conical tank that is 12-meter d...

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Q: 1. Prove that the Taylor series expansion for the function f(x) =x' about x 1 is reduced to x'.

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Q: The general solution of the linear system of differential equation dx Ах dt Is x(t) = ced1tv, + + Cn...

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Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i ...

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Q: Solve the ifferential equation using Ace Laplace transforms- y"-2s'+9 = 6 xe*

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Q: From the following table, estimate the number of students who obtained marks between 40 and 45: Mark...

A: first we make the cumulative frequency table  marks :                      40      50     60       7...

Q: Part: b:Let W be the set of all vectors of the form shown below in parts į and ii. In each part, eit...

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Q: 26) Which segment is shorter for kayaking across the lake, AB or BC ? Explain.

A: Introduction: A triangle is a closed shape that has three angles, three sides, and three vertices. P...

Q: . Find the missing values in the following table : x: 45 50 55 60 65 y: 3.0 2.0 -2.4

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Q: 3. A laser printer uses a laser beam to print copy rapidly for a computer. The laser is positioned b...

A: Given : The transfer function of the system =G(s)=4(s+50)s2+30s+200 To find the unit step response o...

Q: 1. Compute the condition numbers of the following matrices relative to || I. [] [ 3.9 1.6 b. a. 6.8 ...

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Q: Let 1 -1 0 0 0 -1 0 -1 0 1 1 A = 1 -1 a. Draw a directed graph having A as its incidence matrix b. F...

A: Here, we are given the following matrix.      A=1-1000 100-10 010-10 0010-1 For (a), We know that in...

Q: Find the present value of an annuity-immediate which pays 1 at the end of each half-year for five ye...

A: solution:   Given : An annuity-immediate which pays 1 at the end of each half-year for five years, i...

Q: 8. a) Solve by Picard's method dy = 1+ xy, dx y(0) = 1 for x=0.1. Compare it with the exact value of...

A: Here given differential equation is                                                     dydx=1+xy,  ...

Q: Evaluate the following integral by changing the order of integration: S2 Vx sin x dx dy

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.